Question

For each of the following unbalanced equations, calculate how many moles of the second reactant would be required to react completely with exactly \(25.0 \mathrm{g}\) of the first reactant. Indicate clearly the mole ratio used for each conversion. a. \(\mathrm{Mg}(s)+\mathrm{CuCl}_{2}(a q) \rightarrow \mathrm{MgCl}_{2}(a q)+\mathrm{Cu}(s)\) b. \(\operatorname{AgNO}_{3}(a q)+\mathrm{NiCl}_{2}(a q) \rightarrow \operatorname{AgCl}(s)+\mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}(a q)\) c. \(\mathrm{NaHSO}_{3}(a q)+\mathrm{NaOH}(a q) \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) d. \(\mathrm{KHCO}_{3}(a q)+\mathrm{HCl}(a q) \rightarrow\) \(\mathrm{KCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g)\)

Short answer

a. 1.03 moles of CuCl₂ are required to completely react with 25.0g of Mg. b. 0.0735 moles of NiCl₂ are required to completely react with 25.0g of AgNO₃. c. 0.240 moles of NaOH are required to completely react with 25.0g of NaHSO₃. d. 0.249 moles of HCl are required to completely react with 25.0g of KHCO₃.

Step-by-step solution

Calculating moles of Mg

Determine the moles of Mg with the given mass: Mo = mass / molar mass Mg's molar mass is 24.31 g/mol Mo_Mg = 25.0g / 24.31g/mol = 1.03 mol

Calculating moles of CuCl₂

Using the mole ratio of 1:1 between Mg and CuCl₂, we get: Mo_CuCl₂ = 1.03 mol

Results for (a)

1.03 moles of CuCl₂ are required to completely react with 25.0g of Mg. b. Balancing the chemical equation: 2 AgNO₃ (aq) + NiCl₂ (aq) → 2 AgCl (s) + Ni(NO₃)₂ (aq) The balanced equation has a mole ratio of 2:1 between AgNO₃ and NiCl₂.

Calculating moles of AgNO₃

Determine the moles of AgNO₃ using its mass: Molar mass of AgNO₃ is 169.87 g/mol Mo_AgNO₃ = 25.0g / 169.87g/mol = 0.147 mol

Calculating moles of NiCl₂

Using the mole ratio of 2:1 between AgNO₃ and NiCl₂, we get: Mo_NiCl₂ = 0.147 mol / 2 = 0.0735 mol

Results for (b)

0.0735 moles of NiCl₂ are required to completely react with 25.0g of AgNO₃. c. Balancing the chemical equation: NaHSO₃ (aq) + NaOH (aq) → Na₂SO₃ (aq) + H₂O (l) The equation is already balanced with a mole ratio of 1:1

Calculating moles of NaHSO₃

Determine the moles of NaHSO₃ using its mass: Molar mass of NaHSO₃ is 104.07 g/mol Mo_NaHSO₃ = 25.0g / 104.07g/mol = 0.240 mol

Calculating moles of NaOH

Using the mole ratio of 1:1 between NaHSO₃ and NaOH, we get: Mo_NaOH = 0.240 mol

Results for (c)

0.240 moles of NaOH are required to completely react with 25.0g of NaHSO₃. d. Balancing the chemical equation: KHCO₃ (aq) + HCl (aq) → KCl (aq) + H₂O (l) + CO₂ (g) The equation is already balanced with a mole ratio of 1:1

Calculating moles of KHCO₃

Determine the moles of KHCO₃ using its mass: Molar mass of KHCO₃ is 100.12 g/mol Mo_KHCO₃ = 25.0g / 100.12g/mol = 0.249 mol

Calculating moles of HCl

Using the mole ratio of 1:1 between KHCO₃ and HCl, we get: Mo_HCl = 0.249 mol

Results for (d)

0.249 moles of HCl are required to completely react with 25.0g of KHCO₃.

Key concepts

Mole Ratios

Mole ratios are crucial in stoichiometry as they allow chemists to relate amounts of reactants to products in a chemical reaction. Essentially, these ratios come from the coefficients of a balanced chemical equation which indicate the number of moles of each substance involved.
Think of it like a recipe: just as you would need specific amounts of ingredients to bake a cake, mole ratios tell you how many moles of one substance react with or produce moles of another during a chemical reaction.

• To use mole ratios, first ensure that your chemical equation is balanced.
• Identify the coefficients adjacent to the substances you are interested in. These coefficients will be your mole ratios.
• Use these ratios to convert moles of one substance to moles of another.

For instance, in the reaction: \( \mathrm{Mg}(s)+\mathrm{CuCl}_{2}(aq) \rightarrow \mathrm{MgCl}_{2}(aq)+\mathrm{Cu}(s) \), the equation has coefficients of 1:1 for \( \mathrm{Mg} \) and \( \mathrm{CuCl}_{2} \). This implies that 1 mole of magnesium reacts with 1 mole of copper chloride.

Balancing Chemical Equations

Balancing chemical equations is key in stoichiometry as it ensures the law of conservation of mass is obeyed, meaning matter is neither created nor destroyed. A balanced equation has equal numbers of each type of atom on both sides of the equation.
To balance a chemical equation:

• List each type of atom present in the reactants and products.
• Adjust the coefficients—the numbers placed before compounds—to get the same number on each side.
• Only adjust coefficients, never change the subscripts in chemical formulas, as that would change the substances involved.

Consider the equation \( \operatorname{AgNO}_{3}(aq)+\mathrm{NiCl}_{2}(aq) \rightarrow \operatorname{AgCl}(s)+\mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}(aq) \). You must balance it to become:\[ 2\, \operatorname{AgNO}_{3} (aq) + \mathrm{NiCl}_{2} (aq) \rightarrow 2\, \operatorname{AgCl} (s) + \mathrm{Ni} \left(\mathrm{NO}_{3}\right)_{2}(aq) \]Each side now has equal atoms of silver, nitrogen, chlorine, oxygen, and nickel.

Moles Calculation

Calculating moles involves converting the mass of a substance to an amount in moles, using its molar mass. Molar mass, expressed in grams per mole, is the sum of the atomic masses of all atoms in a molecule. This conversion step is vital for using mole ratios in stoichiometric calculations.
The formula used is:\[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]For example, to find the moles of \( \mathrm{Mg} \) given 25g, knowing its molar mass is 24.31 g/mol, calculate:\[ \text{Moles of }\mathrm{Mg} = \frac{25.0 \text{ g}}{24.31 \text{ g/mol}} = 1.03 \text{ mol} \]After obtaining the moles, you can further use mole ratios to calculate how much of another reactant or product is involved in the reaction, facilitating complete conversions between mass and moles.