FINDING THE MASS OF ONE REACTANT, GIVEN THE MASS OF ANOTHER Aqueous solutions of sodium hypochlorite (NaOCl), best known as household bleach, are prepared by reaction of sodium hydroxide with chlorine. How many grams of NaOH are needed to react with 25.0 g of Cl2? 2 NaOH(aq) + Cl2(g) → NaOCl(aq) +

Question

FINDING THE MASS OF ONE REACTANT, GIVEN THE MASS OF ANOTHER

Aqueous solutions of sodium hypochlorite (NaOCl), best known as household bleach, are prepared by reaction of sodium hydroxide with chlorine. How many grams of NaOH are needed to react with 25.0 g of [latex]Cl_{2}[/latex]?

[latex]2 NaOH(aq) + Cl_{2}(g) → NaOCl(aq) + NaCl(aq) + H_{2}O(l)[/latex]

STRATEGY
Finding the relationship between numbers of reactant formula units always requires working in moles, using the general strategy outlined in Figure 3.1.

Accepted Answer

First, find out how many moles of [latex]Cl_{2}[/latex] are in 25.0 g of [latex]Cl_{2}[/latex]. This gram-to-mole conversion is done in the usual way, using the molar mass of [latex]Cl_{2}[/latex] (70.9 g/mol) as the conversion factor:

[latex]25.0 \cancel{g Cl_{2}} × \frac{1 mol Cl_{2}}{70.9 \cancel{g Cl_{2}}} = 0.353 mol Cl_{2}[/latex]

Next, look at the coefficients in the balanced equation. Each mole of [latex]Cl_{2}[/latex] reacts with 2 mol of NaOH, so 0.353 mol of [latex]Cl_{2}[/latex] reacts with 2 × 0.353 = 0.706 mol of NaOH. With the number of moles of NaOH known, carry out a mole-to-gram conversion using the molar mass of NaOH (40.0 g/mol) as a conversion factor to find that 28.2 g of NaOH is required for the reaction:

Grams of NaOH = [latex]0.353 \cancel{mol Cl_{2}} × \frac{2 \cancel{mol NaOH}}{1 \cancel{mol Cl_{2}}} × \frac{40.0 gNaOH}{1 \cancel{mol NaOH}}[/latex]

= 28.2 g NaOH

The problem can also be worked by combining the steps and setting up one large equation:

Grams of NaOH = [latex]25.0 \cancel{g Cl_{2}} × \frac{1 \cancel{mol Cl_{2}}}{70.9 \cancel{g Cl_{2}}} × \frac{2 \cancel{mol NaOH}}{1 \cancel{mol Cl_{2}}} × \frac{40.0 g NaOH}{1 \cancel{mol NaOH}}[/latex]

= 28.2 gNaOH

BALLPARK CHECK
The molar mass of NaOH is about half that of [latex]Cl_{2}[/latex], and 2 mol of NaOH is needed per 1 mol of [latex]Cl_{2}[/latex]. Thus, the needed mass of NaOH will be similar to that of [latex]Cl_{2}[/latex], or about 25 g.

Household bleach is an aqueous solution of NaOCl, made by reaction of NaOH with [latex]Cl_{2}[/latex]

Question 3.7: FINDING THE MASS OF ONE REACTANT, GIVEN THE MASS OF ANOTHER ...

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