Question

What is the molarity of an HCl solution if the reaction of 213 mL of the HCl solution with excess CaCO₃ produces 11.5 L of CO₂ gas at 724 mmHg and 20 °C?

a. 0.284 M
b. 1.420 M
c. 0.568 M
d. 0.710 M

Answer 1

To find the molarity of the HCl solution, use the ideal gas law to calculate moles of CO₂ produced, then use stoichiometry to determine the moles of HCl, and finally divide by the volume of the HCl solution in liters.

Step-by-step explanation:

The molarity of the HCl solution can be determined by following a series of stoichiometry steps. First, we use the ideal gas law to find the number of moles of CO₂, which were produced in the reaction with HCl. The ideal gas law is PV=nRT, where P is the pressure (in atmospheres), V is the volume (in liters), n is the number of moles of gas, R is the ideal gas constant (0.0821 Latm/molK), and T is the temperature (in Kelvin). The pressure must be converted from mmHg to atm by dividing by 760 mmHg/atm.

Once the moles of CO₂ are calculated, we use the stoichiometry of the reaction, which is provided in Example 6.4.1, to find the moles of HCl that reacted. The balanced chemical equation CaCO₃ + 2 HCl → CaCl₂ + CO₂ + H₂O shows us that two moles of HCl produce one mole of CO₂.

With the number of moles of HCl known, we can then divide by the volume of the HCl solution (in liters) that was used to get the molarity. The volume of the HCl solution must be converted from milliliters to liters by dividing by 1000 mL/L before this step. Thus, the molarity is the amount of moles divided by the volume in liters.