Problem 71 - Chemistry and Chemical Reactivity

Question

If \(38.55 \mathrm{mL}\) of HCl is required to titrate \(2.150 \mathrm{g}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) according to the following equation, what is the concentration (mol/L) of the HCl solution? $$\mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{aq})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow 2 \mathrm{NaCl}(\mathrm{aq})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\ell)$$

Step-by-Step Solution

Answer

The concentration of the HCl solution is 1.052 mol/L.

Step 1: Calculate the Moles of Na2CO3

First, calculate the number of moles of \(\mathrm{Na}_2\mathrm{CO}_3\) using its molar mass. The molar mass of \(\mathrm{Na}_2\mathrm{CO}_3\) is calculated as follows: \(2 \times 23.0 + 12.0 + 3 \times 16.0 = 106.0\) g/mol. Therefore, the number of moles of \(\mathrm{Na}_2\mathrm{CO}_3\) is \(\frac{2.150}{106.0} = 0.020283\) moles.

Step 2: Determine the Moles of HCl Required

According to the balanced chemical equation, \(1\) mole of \(\mathrm{Na}_2\mathrm{CO}_3\) reacts with \(2\) moles of \(\mathrm{HCl}\). Therefore, \(0.020283\) moles of \(\mathrm{Na}_2\mathrm{CO}_3\) require \(2 \times 0.020283 = 0.040566\) moles of \(\mathrm{HCl}\).

Step 3: Convert Volume from mL to L

Convert the volume of \(\mathrm{HCl}\) solution from mL to L: \(38.55 \mathrm{mL} = 0.03855 \mathrm{L}.\)

Step 4: Calculate the Concentration of HCl Solution

Finally, calculate the concentration of \(\mathrm{HCl}\) in \(\mathrm{mol/L}\): \(\text{Concentration} = \frac{\text{moles of HCl}}{\text{Volume in L}} = \frac{0.040566}{0.03855} = 1.052\) mol/L.

Key Concepts

Stoichiometry

Stoichiometry is like a recipe for chemical reactions. Just like you need a specific amount of ingredients to bake a cake, you need the right amount of each reactant in a chemical reaction to get the desired product.
In the example exercise, stoichiometry is used to predict the amount of Br>

• Hydrochloric acid (HCl) required to completely react with sodium carbonate (
• Na_2CO_3.

The balanced chemical equation provided tells us exactly how many moles of HCl are needed to react with one mole of Na_2CO_3.
This balanced equation reads: \( \text{Na}_2\text{CO}_3 + 2\text{HCl} \rightarrow 2\text{NaCl} + \text{CO}_2 + \text{H}_2\text{O} \). It shows that for every mole of \( \text{Na}_2\text{CO}_3 \), two moles of \( \text{HCl} \) are needed. So, once you know how many moles of Na_2CO_3 you're starting with, you can easily figure out how many moles of HCl you need.

Molarity Calculation

Molarity is a way of expressing the concentration of a solute in a solution. It's calculated by dividing the number of moles of solute by the volume of the solution in liters. In our example, we need to find the molarity of the HCl solution used in the reaction.
To calculate molarity:

• First, you need to know the number of moles of HCl, which you determined through stoichiometry using the balanced chemical equation.
• Next, convert the volume of HCl solution from milliliters to liters. For the exercise, 38.55 mL becomes 0.03855 L.
• Finally, use the formula for molarity: \[ \text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]

In this exercise, using the formula, the concentration (or molarity) of HCl comes out to be approximately 1.052 mol/L. This tells us how many moles of HCl are present in one liter of solution.

Chemical Equations

Chemical equations represent chemical reactions and show how reactants transform into products. In the exercise, the balanced chemical equation is essential for determining the stoichiometry of the reaction.
A balanced chemical equation must have the same number of every type of atom on both sides of the equation. This satisfies the law of conservation of mass, meaning that mass is neither created nor destroyed in a chemical reaction.
For example:

• The equation \( \text{Na}_2\text{CO}_3 + 2\text{HCl} \rightarrow 2\text{NaCl} + \text{CO}_2 + \text{H}_2\text{O} \) tells us that 1 mole of sodium carbonate reacts with 2 moles of hydrochloric acid to produce 2 moles of sodium chloride, 1 mole of carbon dioxide, and 1 mole of water.
• This equation is balanced because there are equal numbers of each type of atom on both the reactant and product sides.
• Understanding this balance helps us predict the amounts of reactants needed and the amounts of products formed in a given chemical reaction.

Knowing how to read and work with chemical equations is vital for anyone studying chemistry to predict and measure substances involved in reactions.