Stoichiometry Problem: Calculating Reactant Mass

Stoichiometry Problem: Calculating Reactant Mass

Problem Statement

Given the balanced chemical equation:

$SiO<em>2(s) + 4HF(aq) \rightarrow SiF</em>4(g) + 2H_2O(l)$

Determine the mass of hydrogen fluoride (HF) required to react with 45.5 g of silicon dioxide ($SiO_2$).

Given Information

• Mass of silicon dioxide ($SiO_2$) = 45.5 g
• Molar mass of silicon dioxide ($SiO_2$) = 60.09 g/mol
• Molar mass of hydrogen fluoride (HF) = 20.01 g/mol

Objective

Find the mass (in grams) of HF needed to react completely with 45.5 g of $SiO_2$. HF is the 'wanted' species.

Step-by-Step Solution

Step 1: Convert mass of $SiO_2$ to moles

$n<em>{SiO</em>2} = 45.5 \, g \, SiO<em>2 \times \frac{1 \, mol \, SiO</em>2}{60.09 \, g \, SiO<em>2} = 0.7572 \, mol \, SiO</em>2$

Step 2: Convert moles of $SiO_2$ to moles of HF

Using the stoichiometric ratio from the balanced equation (4 moles of HF react with 1 mole of $SiO_2$):

$n<em>{HF} = 0.7572 \, mol \, SiO</em>2 \times \frac{4 \, mol \, HF}{1 \, mol \, SiO_2} = 3.0288 \, mol \, HF$

Step 3: Convert moles of HF to mass of HF

$m_{HF} = 3.0288 \, mol \, HF \times \frac{20.01 \, g \, HF}{1 \, mol \, HF} = 60.586 \, g \, HF$

Rounding to three significant figures, the mass of HF required is 60.6 g.

One-Step Calculation

The entire calculation can be performed in a single step:

$m<em>{HF} = 45.5 \, g \, SiO</em>2 \times \frac{1 \, mol \, SiO<em>2}{60.09 \, g \, SiO</em>2} \times \frac{4 \, mol \, HF}{1 \, mol \, SiO_2} \times \frac{20.01 \, g \, HF}{1 \, mol \, HF} = 60.6 \, g \, HF$

Dimensional Analysis

Note the importance of unit cancellation throughout the calculation, ensuring that the final answer is in the desired unit (grams of HF).