MOLE RATIOS EXPLAINED

Introduction

Mole ratios are a way to describe the proportional relationship between different chemical species in a chemical reaction. Specifically, mole ratios relate the number of moles of one substance involved in a reaction to the number of moles of another substance involved in the same reaction.

A mole is a unit of measurement used in chemistry to describe the amount of a substance. One mole of a substance is equal to its molecular weight in grams. For example, the molecular weight of water (H2O) is approximately 18 grams per mole, which means that one mole of water contains 6.022 x 10^23 molecules and weighs 18 grams.

In a chemical reaction, the mole ratio is determined by the coefficients in the balanced chemical equation. For example, consider the reaction between hydrogen gas (H2) and oxygen gas (O2) to form water:

2H2 + O2 → 2H2O

In this equation, the coefficient for hydrogen gas is 2, meaning that two moles of hydrogen are required for every one mole of oxygen. The coefficient for oxygen gas is 1, meaning that one mole of oxygen is required for every two moles of hydrogen. Therefore, the mole ratio of hydrogen to oxygen in this reaction is 2:1.

Mole ratios are important because they allow chemists to calculate the amounts of reactants and products involved in a reaction. For example, if we know that we have 1 mole of hydrogen gas and want to know how many moles of oxygen gas are required to completely react with it, we can use the mole ratio to calculate this. Since the mole ratio of hydrogen to oxygen is 2:1, we know that we need 0.5 moles of oxygen gas to react completely with 1 mole of hydrogen gas.

Mole ratios are also useful in determining the limiting reactant in a chemical reaction. The limiting reactant is the reactant that is completely consumed in a reaction, and limits the amount of product that can be formed. By comparing the mole ratios of the reactants in a reaction, we can determine which reactant will be the limiting reactant.

In summary, mole ratios are a way to describe the proportional relationship between different chemical species in a chemical reaction, and are determined by the coefficients in the balanced chemical equation. They are important for calculating reactant and product amounts, as well as determining the limiting reactant in a reaction.

 

 

A) Number of entities calculations

Chemistry deals with a vast range of entities, including atoms, molecules, ions, and particles. The number of entities in chemistry can be determined using various calculations, depending on the specific entity being considered.

Here are some common calculations used to determine the number of entities in chemistry:

1) Atoms in a substance: The number of atoms in a substance can be determined using Avogadro’s number, which is 6.022 x 10^23 atoms per mole. To calculate the number of atoms in a given substance, divide the mass of the substance by its molar mass and then multiply by Avogadro’s number.

For example, to determine the number of atoms in 1.0 g of hydrogen gas (H2), the calculation would be:

(1.0 g H2 / 2.016 g/mol H2) x (6.022 x 10^23 atoms/mol) = 2.99 x 10^23 atoms of H2

 

2) Molecules in a substance: The number of molecules in a substance can be determined using the same calculation as for atoms, but instead of using the molar mass of the element, use the molar mass of the molecule.

For example, to determine the number of water molecules in 2.0 g of water (H2O), the calculation would be:

(2.0 g H2O / 18.015 g/mol H2O) x (6.022 x 10^23 molecules/mol) = 6.70 x 10^23 molecules of H2O

 

3) Ions in a substance: The number of ions in a substance can be determined using the molarity (M) of the solution and the number of ions per molecule of the solute. For example, if the solute is NaCl, which dissociates into one Na+ ion and one Cl- ion per molecule, the calculation would be:

Number of ions = M x volume (in liters) x number of ions per molecule

For example, if you have a 0.1 M solution of NaCl with a volume of 1 liter, the calculation would be:

Number of ions = 0.1 M x 1 L x 2 ions/molecule = 0.2 moles of ions Number of ions = 0.2 moles x 6.022 x 10^23 ions/mol = 1.20 x 10^23 ions

 

 

B) Amount of substance Calculations

The amount of substance is typically measured in moles (mol). A mole is defined as the amount of substance that contains as many elementary entities (such as atoms, molecules, or ions) as there are atoms in 12 grams of pure carbon-12.

To determine the amount of substance in a sample, you need to know the mass of the sample and the molar mass of the substance. The molar mass is the mass of one mole of the substance and is expressed in grams per mole (g/mol).

The formula to calculate the amount of substance (n) is:

n = m / M

where:

• n is the amount of substance in moles
• m is the mass of the substance in grams
• M is the molar mass of the substance in grams per mole

For example, if you have a sample of sodium chloride (NaCl) with a mass of 5 grams, you can calculate the amount of substance as follows:

1) Determine the molar mass of NaCl. The molar mass of NaCl is the sum of the atomic masses of sodium (Na) and chlorine (Cl), which are 22.99 g/mol and 35.45 g/mol, respectively. Therefore, the molar mass of NaCl is 22.99 + 35.45 = 58.44 g/mol.

2) Plug in the values into the formula:

n = m / M

n = 5 g / 58.44 g/mol n = 0.0854 mol

Therefore, the amount of substance in the sample of NaCl is 0.0854 mol.

 

C) Mass calculations 

In order to determine the mass of a substance in a stoichiometry problem, you can use the following steps:

 

How many grams of carbon dioxide (CO2) are produced when 25 grams of propane (C3H8) are completely burned in oxygen (O2)?

First, we need to balance the chemical equation:

C3H8 + 5O2 -> 3CO2 + 4H2O

Then, we can use the balanced equation to determine the number of moles of CO2 produced:

1 mol C3H8 produces 3 mol CO2

25 g C3H8 / 44.1 g/mol C3H8 = 0.567 mol C3H8

0.567 mol C3H8 x 3 mol CO2 / 1 mol C3H8 = 1.70 mol CO2

Finally, we can convert the number of moles of CO2 to grams:

1.70 mol CO2 x 44.0 g/mol CO2 = 74.8 g CO2

Therefore, 25 grams of propane would produce 74.8 grams of carbon dioxide when completely burned in oxygen.

 

What mass of sodium hydroxide (NaOH) is needed to react completely with 10.0 grams of sulfuric acid (H2SO4) to produce sodium sulfate (Na2SO4), water (H2O), and carbon dioxide (CO2)?

First, we need to balance the chemical equation:

H2SO4 + 2NaOH -> Na2SO4 + 2H2O + CO2

Then, we can use the balanced equation to determine the number of moles of NaOH needed:

1 mol H2SO4 reacts with 2 mol NaOH

10.0 g H2SO4 / 98.1 g/mol H2SO4 = 0.102 mol H2SO4

0.102 mol H2SO4 x 2 mol NaOH / 1 mol H2SO4 = 0.204 mol NaOH

Finally, we can convert the number of moles of NaOH to grams:

0.204 mol NaOH x 40.0 g/mol NaOH = 8.16 g NaOH

Therefore, 10.0 grams of sulfuric acid would react completely with 8.16 grams of sodium hydroxide to produce sodium sulfate, water, and carbon dioxide.

 

D) Concentration calculations

One important aspect of stoichiometry is determining the concentration of a reactant or product in a solution.

To calculate the concentration of a substance, we use the following formula:

Concentration = (moles of substance) / (volume of solution)

Here are the steps to follow to calculate the concentration of a substance in stoichiometry:

1. Write a balanced chemical equation for the reaction.
2. Identify the reactant or product whose concentration you want to calculate.
3. Determine the number of moles of the reactant or product involved in the reaction using the stoichiometric coefficients from the balanced equation.
4. Measure the volume of the solution containing the reactant or product whose concentration you want to calculate.
5. Plug the values from steps 3 and 4 into the concentration formula to calculate the concentration of the reactant or product.

Let’s take an example to illustrate this process. Consider the reaction:

2 HCl(aq) + Na2CO3(aq) -> 2 NaCl(aq) + H2O(l) + CO2(g)

Suppose we want to calculate the concentration of NaCl in a solution that contains 0.025 moles of Na2CO3 in 250 mL of solution. Here are the steps to follow:

1. The balanced equation tells us that 2 moles of NaCl are produced for every 1 mole of Na2CO3 consumed.
2. We want to calculate the concentration of NaCl, which is a product of the reaction.
3. Since 2 moles of NaCl are produced for every 1 mole of Na2CO3 consumed, we know that the amount of NaCl produced is 2 x 0.025 = 0.05 moles.
4. The volume of the solution is 250 mL, which is equivalent to 0.25 L.
5. Using the concentration formula, we can calculate the concentration of NaCl as follows:

Concentration of NaCl = (0.05 moles) / (0.25 L) = 0.20 M

Therefore, the concentration of NaCl in the solution is 0.20 M.

 

E) Volume calculations

the volume of a reactant or product can be determined by using the ideal gas law, which relates the pressure, volume, temperature, and number of moles of a gas. Here are two examples of how to use the ideal gas law to calculate the volume of a gas in stoichiometry:

Example 1: Hydrogen gas is produced by the reaction of 5.00 g of magnesium with excess hydrochloric acid at standard temperature and pressure (STP). What is the volume of hydrogen gas produced?

Step 1: Write the balanced chemical equation: Mg(s) + 2HCl(aq) -> MgCl2(aq) + H2(g)

Step 2: Calculate the number of moles of magnesium: n(Mg) = m/Mw = 5.00 g / 24.31 g/mol = 0.206 mol

Step 3: Determine the limiting reactant: n(HCl) = excess n(H2) = n(Mg) x (1 mol H2 / 1 mol Mg) = 0.206 mol

Since Mg is the limiting reactant, all of its moles will be used up to produce H2 gas.

Step 4: Use the ideal gas law to calculate the volume of H2 gas: PV = nRT V = nRT/P = (0.206 mol)(0.0821 L·atm/mol·K)(273 K) / 1 atm = 4.94 L

Therefore, the volume of H2 gas produced is 4.94 L.

 

Example 2: Methane gas (CH4) reacts with excess oxygen gas (O2) to produce carbon dioxide gas (CO2) and water vapor (H2O) at 25°C and 1.00 atm. If 2.00 L of methane gas is consumed in the reaction, what is the volume of carbon dioxide gas produced?

Step 1: Write the balanced chemical equation: CH4(g) + 2O2(g) -> CO2(g) + 2H2O(g)

Step 2: Calculate the number of moles of methane: n(CH4) = PV/RT = (1.00 atm)(2.00 L) / (0.0821 L·atm/mol·K)(298 K) = 0.0846 mol

Step 3: Use stoichiometry to determine the number of moles of CO2 produced: n(CO2) = n(CH4) x (1 mol CO2 / 1 mol CH4) = 0.0846 mol

Step 4: Use the ideal gas law to calculate the volume of CO2 gas: PV = nRT V = nRT/P = (0.0846 mol)(0.0821 L·atm/mol·K)(298 K) / 1.00 atm = 1.97 L

Therefore, the volume of CO2 gas produced is 1.97 L.

 

F) Percentage yield of product calculations