Complete each nuclear fission reaction.

Answer:

PV=(n

total

​

)RT

(1)(V)=(0.3+0.2)(0.0821)(400)=(0.5)(400)(0.0821)=2×(8.21)=16.4litres

The number 38.7 x 10⁷ is already in scientific notation

The coefficient is 38.7 and the exponent is 7.

In the given number, 38.7 x  10⁷,  the coefficient is 38.7, which is a decimal number between 1 and 10.

The exponent of 10 is 7, which tells us to move the decimal point seven places to the right to get the actual value of the number.

So, 38.7 x 10⁷ can be expanded as follows:

38.7 x  10⁷= 38.7 000 000

we moved the decimal point seven places to the right and filled the empty spaces with zeros. This gives us the actual value of the number in standard form.

Scientific notation, also referred to as standard form or exponential notation, is a format for succinctly expressing very large or very tiny numbers. It is predicated on the notion that a number can be represented as the result of a coefficient and a multiple of 10.

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the maximum amount of product that can be formed is 124.39 g SO₃, and there will be 36.8 g of excess O₂ left over.

To find the amount of excess reagent, you need to first determine which reactant is limiting and which is in excess.

Determine the limiting reagent:

Use stoichiometry to determine how much product can be formed from each reactant:

mol SO2:

2 SO₂ + O₂ -> 2 SO₃

2 mol SO₃/2 mol SO₂ = 1 mol SO₃/mol SO₂

1 mol SO₃ = 80.06 g SO₍₃₎

From 2.7 mol O₂

2 SO₂ + O₂ -> 2 SO₃

1 mol SO₃/1 mol O₂ = 1 mol SO₃/mol O₂

1 mol SO₃ = 80.06 g SO₃

2.7 mol O₂ x (1 mol SO₂/1 mol O₂) x (80.06 g SO₂/mol SO₂) = 216.45 g SO₂

Since the amount of SO₂ produced from 3.1 mol of SO₂ is less than the amount produced from 2.7 mol of O₂, SO₂ is the limiting reagent.

Calculate the amount of excess reagent:

To find the amount of excess O₂, use the balanced equation to determine how much O₂ is required to react with all of the SO₂:

2 SO₂ + O₂ -> 2 SO

3.1 mol SO2 x (1 mol O₂/2 mol SO2) = 1.55 mol O₂

Subtract the amount of O₂ used from the initial amount of O₂:

2.7 mol O₂ - 1.55 mol O2 = 1.15 mol O₂

Finally, convert the excess O₂ to mass:

1.15 mol O₂ x 32.00 g/mol = 36.8 g O₂

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Poaching tigers for their skins = overexploitation of resources, discharging sewage= water pollution, increasing the release of greenhouse gases = climate change.

The Earth's atmosphere contains molecules called greenhouse gases that hold heat in place and keep it from escaping into space. These gases, which also include water vapor, methane, and carbon dioxide, operate as a blanket over the globe to keep it warm and habitable.

Due to the pressure it places on the tigers' population, tiger poaching for its skin is an activity that results in overexploitation of resources. Animals can go extinct as a result of poaching, which is the illegal hunting and killing of animals. Tiger populations are decreased and their habitat is disturbed when they are poached for their skins.

Water pollution results from sewage discharge into water bodies. Water sources that have been contaminated by sewage, which contains dangerous germs and chemicals, are unsuitable for consumption by both people and wildlife. Moreover, this can cause eutrophication, which is the development of algae and other plant life in water bodies as a result of an overabundance of nutrients.

Climate change is caused by an increase in the emission of greenhouse gases like carbon dioxide and methane. The atmosphere of the Earth warms as a result of these gases trapping heat. This may have a number of harmful ecological repercussions, such as increased extreme weather occurrences, increasing sea levels, and the loss of habitat for numerous plant and animal species.

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Explanation:

Formic acid (HCOOH) reacts with sodium hydroxide (NaOH) to form sodium formate (HCOONa) and water. The balanced chemical equation is:

HCOOH + NaOH → HCOONa + H2O

The reaction is a strong acid-strong base titration. We can use the following equation to calculate the concentration of formate ion (HCOO^-) in the resulting solution:

[HCOO^-] = [OH^-] - [HCOOH]

where [OH^-] is the concentration of hydroxide ion and [HCOOH] is the concentration of formic acid before the reaction.

Before the reaction, the solution contains 0.25 mol/L of formic acid in 55.0 mL, or 0.25 mol/L × 0.055 L = 0.01375 mol of formic acid. The solution also contains 0.12 mol/L of sodium hydroxide in 75.0 mL, or 0.12 mol/L × 0.075 L = 0.009 mol of sodium hydroxide.

Since the reaction between formic acid and sodium hydroxide is a 1:1 reaction, all the 0.009 mol of sodium hydroxide will react with 0.009 mol of formic acid, leaving 0.00475 mol of formic acid unreacted.

[HCOO^-] = [OH^-] - [HCOOH]

[OH^-] = [NaOH] = 0.12 mol/L × 0.075 L / 0.13 L = 0.0692 mol/L

[HCOO^-] = 0.0692 mol/L - 0.00475 mol/L = 0.0645 mol/L

Now we can calculate the pH of the resulting solution using the Ka expression for formic acid:

Ka = [HCOO^-][H3O^+]/[HCOOH]

[H3O^+] = Ka × [HCOOH] / [HCOO^-]

[H3O^+] = 1.77 × 10^-4 × 0.00475 mol/L / 0.0645 mol/L

[H3O^+] = 1.29 × 10^-5 mol/L

pH = -log[H3O^+]

pH = -log(1.29 × 10^-5)

pH = 4.89

Therefore, the resulting pH is 4.89.

The net ionic equation for the reaction is:

2Fe3+(aq) + 3S2-(aq) → Fe2S3(s)

What is Ionic Equation?

An ionic equation is a chemical equation that shows the chemical species as their respective ions in a solution. In other words, an ionic equation only includes the ions that participate in the chemical reaction, and excludes any spectator ions that do not participate in the reaction.

The net ionic equation shows only the species that participate in the reaction and omits the spectator ions (ions that appear on both sides of the equation without undergoing a change).

First, let's write the balanced chemical equation for the reaction:

Fe2(SO4)3(aq) + 3K2S(aq) → Fe2S3(s) + 3K2SO4(aq)

To write the net ionic equation, we need to identify the ions that are present in aqueous solution and that participate in the reaction. These are:

Fe2+(aq), SO42-(aq), K+(aq), and S2-(aq)

The balanced ionic equation is:

2Fe3+(aq) + 3SO42-(aq) + 6K+(aq) + 3S2-(aq) → Fe2S3(s) + 3K2SO4(aq)

To obtain the net ionic equation, we eliminate the spectator ions, which are the potassium and sulfate ions that appear on both sides of the equation:

2Fe3+(aq) + 3S2-(aq) → Fe2S3(s)

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To solve this problem,  the ideal gas law equation can be used. The volume of the balloon will come to 79.9 liters.

The ideal gas law is a fundamental equation in physics and chemistry that describes the behavior of ideal gases under various conditions. The law is expressed mathematically as:

PV = nRT

where P is the pressure of the gas, V is the volume it occupies, n is the number of moles of gas, T is the temperature of the gas in Kelvin, and R is the universal gas constant.

First, we need to convert the temperature from Celsius to Kelvin:

T = 20°C + 273.15 = 293.15 K

Next, we need to find the value of R, which is 0.0821 L·atm/mol·K for ideal gases.

We also know that the pressure is standard pressure, which is 1 atm.

Plugging in all the values, we get:

V = (nRT) / P

V = (3.2 mol * 0.0821 L·atm/mol·K * 293.15 K) / 1 atm

V = 79.9 L

Therefore, the volume of the balloon is 79.9 liters.

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The ΔS° value for the reaction KCl(s) → K+(aq) + Cl−(aq) is ΔS° > 0, as the products have a higher degree of disorder than the reactant due to an increase in the number of particles in solution. Hence the correct option is (C) ΔS° > 0.

The ΔS° value for a reaction represents the change in the entropy of the system, which is a measure of the disorder or randomness of the system. The reaction KCl(s) → K+(aq) + Cl−(aq) involves a solid compound breaking down into two separate aqueous ions, which means that the products have a higher degree of disorder than the reactant. This increase in the number of particles in solution results in an increase in entropy, which means that ΔS° > 0. Option (A) is incorrect because the reaction involves a change in state, which results in an increase in entropy. Option (B) is incorrect because it represents the relationship between enthalpy and entropy, not the ΔS° value for this particular reaction. Option (D) is incorrect because the reaction results in an increase in entropy, not a decrease. Option (E) is incorrect because the given information is sufficient to predict the sign of ΔS°.

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It is important to note that lead poisoning is a serious condition that requires prompt medical attention. If you or someone you know has ingested lead nitrate, seek medical attention immediately.

What is Lead Nitrate?

Lead nitrate is an inorganic compound with the chemical formula Pb(NO3)2. It is a colorless, odorless, and crystalline solid that is highly soluble in water. Lead nitrate is commonly used in various industrial processes, including the manufacture of lead-based explosives, pigments, and pyrotechnics.

Swallowing soluble lead nitrate, Pb(NO3)2, can lead to lead poisoning, which can cause various health problems, including abdominal pain, vomiting, diarrhea, seizures, and in severe cases, coma or death. If someone has swallowed this compound, it is important to seek medical attention immediately.

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Answer:

Products will be Ga2Br2 and CaS3 (Double Displacement Reaction)

The ΔH for the given reaction is +204.8 kJ. This indicates that the reaction is endothermic, which absorbs heat from the surroundings.

To determine the AH for the given reaction, we can use the following steps:

Write the balanced chemical equation for the reaction.

2CO(g) + 2NO(g) ⇒ 2CO₂(g) + N₂(g)

Use the given equations to write the overall reaction as a combination of the given reactions. We can do this by reversing equation (a) and multiplying equation (b) by 2 so that the reactants and products match the overall reaction.

2CO₂(g) ⇒ 2CO(g) + O₂(g) ΔH = +566.0 kJ (reversed)

2N₂(g) + 2O₂(g) ⇒ 4NO(g) ΔH = -2(180.6 kJ) = -361.2 kJ (multiplied by 2)

Overall reaction:

2CO(g) + 2NO(g) ⇒ 2CO₂(g) + N₂(g) ΔH = ?

Step 3: Add the ΔH values for the individual reactions to obtain the ΔH for the overall reaction.

ΔH = (+566.0 kJ) + (-361.2 kJ) = +204.8 kJ

Therefore,  the ΔH for the given reaction is +204.8 kJ. This indicates that the reaction is endothermic, meaning that it absorbs heat from the surroundings., meaning that it absorbs heat from the surroundings.

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The products of the reaction are iron (II) carbonate and copper (II) nitrate.

[tex]Fe(NO_3)_2 + Cu_2CO_3 - > FeCO_3 + 2Cu(NO_3)_2[/tex]

An inorganic substance with the molecular formula Fe(NO₃)₂ is iron (II) nitrate. It is a crystalline green substance that can be dissolved in water. Iron or iron oxide can be used to combine with nitric acid to create iron (II) nitrate, which is a salt of both iron and nitric acid.

It is frequently used as an iron supply in chemical processes as well as a starting point for the creation of other iron compounds. Additionally, the creation of pigments, dyes, and catalysts can be accomplished using iron (II) nitrate.

However, it needs to be handled carefully because it is a potent oxidizer and, if not treated correctly, can irritate the skin and eyes.

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Your speed could change in several ways as you jog along a park's path. Option 2.

One possible way is that you could speed up if you increase your pace or start running instead of jogging. This could happen if you feel more energized, motivated, or if you need to catch up with someone.

Conversely, your speed could slow down if you get tired, experience muscle fatigue, or encounter an uphill section of the path that requires more effort. Other factors such as weather conditions, terrain, or distractions can also affect your speed.

Therefore, the correct answer would be "all of these, except none of these," as there are various factors that can cause changes in your jogging speed along a park's path.

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Answer:

To find the molarity of the new solution, we need to use the equation:

M1V1 = M2V2

Where:

M1 = initial molarity = 3.00 M

V1 = initial volume = 15.0 mL

M2 = final molarity (what we're solving for)

V2 = final volume = 30.0 mL

Rearranging the equation to solve for M2:

M2 = (M1V1)/V2

M2 = (3.00 M * 15.0 mL)/30.0 mL

M2 = 1.50 M

Therefore, the molarity of the new solution is 1.50 M.

Answer:

1.00 M

Explanation:

Molarity is defined as the number of moles of solute per liter of solution. When a solution is diluted, the number of moles of solute remains constant, but the volume of the solution increases. Therefore, the molarity of the solution decreases.

In this case, the initial number of moles of solute in the 15.0 mL of 3.00 M hydrochloric acid solution is (15.0 mL) * (3.00 mol/L) * (1 L/1000 mL) = 0.045 mol.

After dilution, the volume of the solution increases to 30.0 mL + 15.0 mL = 45.0 mL. The molarity of the diluted solution is (0.045 mol) / (45.0 mL) * (1000 mL/L) = 1.00 M.

So, the molarity of 30.0 mL of hydrochloric acid solution after 15.0 mL of a 3.00 M solution has been diluted is 1.00 M.

The number of moles of CO contained in the 20.0 L tank at 93 °C and 4.52 atm is 3.01 moles

Ideal gas equation is given as follow:

PV = nRT

Where

With the above formula, we can obtain the number of mole of CO in the tank. This is shown below:

PV = nRT

4.52 × 20 = n × 0.0821 × 366

Divide both sides by (0.0821 × 366)

n = (4.52 × 20) / (0.0821 × 366)

n = 3.01 moles

Thus, we can conclude that the number of mole of the gas is 3.01 moles. The correct answer is the 3rd option

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The bond energy is -183 kJ/ mol for the given reaction and bond energies for the reaction. The reaction is exothermic.

Atoms bond together to create compounds because doing so allows them to achieve lower energies than they would have as individual atoms. A quantity of energy equivalent to the difference between the energies of the bonded and separated atoms is released, typically as heat. That is, linked atoms have less energy than individual atoms. Energy is always released when atoms combine to form a compound, and the compound has a reduced overall energy.

When a chemical reaction happens, molecular bonds are broken and new bonds are formed, resulting in the formation of new molecules.

Change is energy(ΔE) = ΣΔBE (Products) - ΣΔBE (Reactant)

ΔE = (432+ 239) - 2×427

ΔE = -183 kJ/ mol

Therefore it is exothermic reaction.

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Answer:

We would expect stars near the edge of the galaxy to rotate slower than stars near the center. This is because the rotational speed of objects in a rotating system depends on their distance from the center of rotation. Stars near the center of the galaxy are closer to the gravitational center of the galaxy's mass, so they feel a stronger gravitational pull and rotate faster. Stars near the edge are farther from the center, so they feel a weaker gravitational pull and rotate slower. This results in a gradient of rotational speeds, with the fastest speeds near the galactic center and slower speeds near the edges.

The balanced chemical equation for the reaction between antimony trioxide (Sb2O3) and carbon monoxide (CO) is:

Sb2O3 + 3CO → 2Sb + 3CO2

From the equation, we can see that 1 mole of Sb2O3 reacts with 3 moles of CO to produce 3 moles of CO2. The molar mass of Sb2O3 is 291.52 g/mol, so 0.465 g of Sb2O3 is equal to 0.465 g / 291.52 g/mol = 0.001592 mol.

Since 1 mole of Sb2O3 reacts with 3 moles of CO, we need 3 * 0.001592 = 0.004776 mol of CO to react completely with 0.465 g of Sb2O3.

The molar mass of CO is 28.01 g/mol, so 0.004776 mol of CO is equal to 0.004776 mol * 28.01 g/mol = 0.1338 g of CO.

Therefore, 0.465 g of Sb2O3 will produce 0.1338 g of CO. To convert this to liters of CO at a given temperature and pressure, we would need to know the volume of 0.1338 g of CO under those conditions using the ideal gas law.

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The amount of lithium nitrate needed to make 230 grams of lithium sulfate depends on the amount of lead (IV) sulfate provided and is equal to half of the moles of lithium sulfate produced, which is 2.091/2 = 1.046 mol. The mass of lithium nitrate required can be calculated using its molar mass.

To calculate the amount of lithium nitrate required to make 230 grams of lithium sulfate, we can use the following steps:

Calculate the molar mass of lithium sulfate:

Li2SO4: 2(6.94 g/mol) + 1(32.06 g/mol) + 4(16.00 g/mol) = 109.94 g/mol

Determine the number of moles of lithium sulfate:

n = m/M = 230 g / 109.94 g/mol = 2.091 mol

Since 2 moles of lithium sulfate are produced for every 1 mole of lead (IV) sulfate, we need 2.091/2 = 1.046 mol of lead (IV) sulfate to react with the lithium sulfate.

Calculate the mass of lead (IV) sulfate required:

m = nM = 1.046 mol x Pb(SO4)2 molar mass (assuming it's provided)

From the balanced equation, we know that for every 2 moles of lithium sulfate, we need 1 mole of lithium nitrate.

The amount of lithium nitrate needed to make 230 grams of lithium sulfate depends on the amount of lead (IV) sulfate provided and is equal to half of the moles of lithium sulfate produced, which is 2.091/2 = 1.046 mol. The mass of lithium nitrate required can be calculated using its molar mass.

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The dependent variable in this experiment would be the height of the explosion.

What is Soda?

Soda, also known as carbonated beverage or fizzy drink, is a drink that contains carbon dioxide gas dissolved in water, along with other ingredients such as sweeteners, flavors, and preservatives. The carbon dioxide gas is responsible for the characteristic fizz or bubbles that soda is known for.

In an experiment, the dependent variable is the variable that is being measured or observed and is expected to change in response to the independent variable. In this experiment, the independent variable is the type of soda used, while the dependent variable is the height of the explosion. The height of the explosion is what the experimenters will measure and observe to determine the effect of the independent variable (type of soda) on the outcome (height of explosion). Therefore, the height of the explosion is the dependent variable in this experiment.

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The flow rate of fuel from the pump is 0.25 liters/second.

To find the flow rate of fuel from the pump, we need to determine the volume of fuel that is dispensed per unit of time.

75 liters = 0.075 cubic meters

Mass = volume x density

Mass = 0.075 cubic meters x 680 kg/cubic meter

Mass = 51 kg

we can convert the time it takes to fill the tank from minutes to seconds:

5 minutes = 300 seconds

Finally, we can calculate the flow rate of fuel from the pump:

Flow rate = mass/time

Flow rate = 51 kg / 300 seconds

Flow rate = 0.17 kg/second

Since we know the relative density of the fuel is 0.68, we can convert the flow rate from kilograms to liters:

Flow rate = mass/density

Flow rate = 0.17 kg / 0.68 kg/liter

Flow rate = 0.25 liters/second

The flow rate of fuel from the pump is 0.25 liters/second.

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substituting zirconium ions in the  [tex]MgO[/tex] lattice will create cation vacancies and increase the energy of the system. This will affect the stoichiometry and electrical properties of the material.

Substituting zirconium ions in the [tex]MgO[/tex] lattice will result in cation vacancies because the ionic radius of zirconium [tex](Zr4+)[/tex] is larger than that of magnesium [tex](Mg2+)[/tex].

The larger zirconium ions will not fit perfectly in the magnesium sites, and therefore some magnesium ions will need to move away from the lattice to accommodate the larger zirconium ions. This creates vacancies on the cation lattice.

The energy required to form a Schottky defect in [tex]MgO[/tex] is  [tex]6[/tex] eV, which is a measure of the stability of the crystal lattice.

The Schottky defect creates both cation and anion vacancies, and it is thermodynamically favorable at high temperatures, where the entropy of the system can offset the energy cost of the defect formation.

However, in the absence of entropy effects, the formation of cation vacancies due to zirconium substitution will increase the energy of the system. The increase in energy will depend on the concentration of cation vacancies and the extent of zirconium substitution.

Therefore, substituting zirconium ions in the [tex]MgO[/tex] lattice will create cation vacancies and increase the energy of the system. This will affect the stoichiometry and electrical properties of the material.

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Answer:

C₅H₁₀.

Explanation:

To determine the molecular formula of the compound, we need to know the molar mass of the compound. Since the empirical formula is CH₂, the empirical molar mass can be calculated as:

Empirical molar mass = 12.01 g/mol (atomic mass of C) + 2(1.01 g/mol) (atomic mass of H)

Empirical molar mass = 14.03 g/mol

The molecular mass of the compound is given as 70.15 g/mol. To find the molecular formula, we need to know how many empirical units are present in the molecule. This can be calculated by dividing the molecular mass by the empirical molar mass:

Number of empirical units = Molecular mass / Empirical molar mass

Number of empirical units = 70.15 g/mol / 14.03 g/mol

Number of empirical units = 5

This means that there are 5 empirical units (CH₂) present in the molecular formula of the compound. Therefore, the molecular formula is:

Molecular formula = 5(CH₂) = C₅H₁₀

Thus, the molecular formula of the compound is C₅H₁₀.

An endothermic reaction is a chemical reaction that requires energy input to proceed, meaning the products have higher potential energy than the reactants.

Endothermic reactions absorb heat from the surroundings, resulting in a decrease in temperature. In endothermic reactions, the energy term in the enthalpy change equation is positive.

An example of an endothermic equation is the reaction between baking soda and citric acid to produce carbon dioxide gas, water, and sodium citrate:

NaHCO3 + H3C6H5O7 → Na3C6H5O7 + 3H2O + CO2

This reaction requires energy input in the form of heat to break the bonds between the reactants and initiate the reaction. The reaction absorbs heat from the surroundings, making it feel cool to the touch.

What do you understand by the endothermic reaction? describe in brief.

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The half-life of radon-222 is 4 days, which means that after each 4-day period, the amount of radon-222 in a sample is halved.

After 8 days, only 25 g of the 100 g sample of radon-222 would be remaining. After 8 days, there have been two half-life periods. Therefore, we can find the amount of radon-222 remaining after 8 days using the following formula:

Amount remaining = (Initial amount) x (1/2)^(number of half-life periods)

Initial amount = 100 g

Number of half-life periods = 8 days / 4 days per half-life = 2 half-life periods

Substituting these values into the formula gives:

Amount remaining = 100 g x (1/2)² = 100 g x (1/4) = 25 g

Therefore, after 8 days, only 25 g of the 100 g sample of radon-222 would be remaining.

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The molarity of potassium hydroxide is 1 mol/dm³.

Molarity is a measure of concentration, expressing the number of moles of a solute per litre of solution. It is denoted by the symbol M and is an important concept in chemistry, especially when dealing with solutions. Molarity is related to the molar mass of the solute and the density of the solution. It is a useful tool for measuring the amount of a particular solute in a given solution.

To calculate the molarity of potassium hydroxide, we must first calculate the moles of HCl and KOH.

First, we calculate the moles of HCl. We use the formula moles = concentration x volume.

HCl: 0.15 moldm³ x (31.40/1000) = 0.00471 moles

Next, we calculate the moles of KOH.

KOH: (20/1000) = 0.02 moles

Now we can calculate the molarity of KOH. We use the formula molarity = moles/volume.

KOH: 0.02/0.02 = 1 mol/dm³

Therefore, the molarity of potassium hydroxide is 1 mol/dm³.

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We would need to measure 7.5 mL of the 2.0M solution of KNO₃ and then add enough solvent to get the total volume up to 100.0 mL.

Volume is a unit used to describe how much three-dimensional space an object or substance occupies. By multiplying the length, breadth, and height of an object or substance, as well as additional mathematical formulas tailored to the shape of the object or substance, one can determine the volume of the thing or substance.

We can use the following formula to create a solution:

M1V1 = M2V2

where M1 denotes the starting concentration, V1 the starting volume, M2 the ending concentration, and V2 the ending volume.

In this instance, we want to make a 100.0 mL 0.15M KNO₃ solution using a 2.0M KNO₃ solution.

When these values are added to the formula, we obtain:

(2.0 M) V1 = (0.15 M) (100.0 mL) 

When we solve for V1, we get:

V1 = (0.15 M) (100.0 mL) / (2.0 M) (2.0 M)

V1 = 7.5 mL

So, to prepare 100.0 mL of a 0.15M solution of KNO₃, we would need to measure 7.5 mL of the 2.0M solution of KNO₃ and then add enough solvent to get the total volume up to 100.0 mL.

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The length of side BC is approximately 1.82 units.

To find the length of side BC, we can use trigonometry. Since we know two angles of the triangle, we can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle ABC:

Angle ABC = 180 - 90 - 70 = 20 degrees

We can now use the trigonometric function tangent to find the length of BC:

tan(20) = BC/5

Solving for BC, we get:

BC = 5*tan(20) ≈ 1.82 units

The length of side BC is approximately 1.82 units.

The connections between the sides and angles of triangles are the subject of the mathematical discipline of trigonometry. It is helpful in several disciplines, including navigation, physics, engineering, and building.

Sine, cosine, and tangent are the three fundamental trigonometric functions that link the ratios of the lengths of the sides of a right triangle to the angles opposite those sides.

The ratio of the length of the side opposing the angle to the length of the hypotenuse is known as the sine of an angle. (the longest side of the right triangle).

The proportion of the neighboring side's length to the hypotenuse's length is known as the cosine of an angle.

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