A 10.0 mL sample of 12.1 M hydrochloric acid is added to 90.0 mL of distilled water and added to a sealed 1.04 L reaction vessel containing 1.463 g of calcium hydrogencarbonate at 22.1ºC and 743 mmHg. What is the pressure of carbon dioxide gas?

To find the pressure of carbon dioxide gas, we need to use the ideal gas law equation:

PV = nRT

Where:
P = Pressure
V = Volume
n = number of moles
R = ideal gas constant
T = temperature

First, let's find the number of moles of carbon dioxide produced in the reaction.

Calcium hydrogencarbonate is a solid substance and does not participate in the gas phase of the reaction. Therefore, we can ignore it in our calculation.

The balanced chemical equation for the reaction between hydrochloric acid and calcium hydrogencarbonate is:

2HCl + Ca(HCO3)2 -> CaCl2 + 2CO2 + 2H2O

According to the equation, 2 moles of hydrochloric acid produce 2 moles of carbon dioxide gas. So the number of moles of carbon dioxide gas produced will be the same as the number of moles of hydrochloric acid.

To find the number of moles of hydrochloric acid, we use the formula:

moles = concentration (M) × volume (L)

Given:
- Volume of hydrochloric acid = 10.0 mL = 0.01 L
- Concentration of hydrochloric acid = 12.1 M

moles of hydrochloric acid = 12.1 M × 0.01 L
moles of hydrochloric acid = 0.121 moles

Therefore, the number of moles of carbon dioxide gas produced is also 0.121 moles.

Now, let's solve for the pressure of carbon dioxide gas using the ideal gas law equation:

PV = nRT

Given:
- Volume of the reaction vessel = 1.04 L
- Temperature = 22.1ºC = 22.1 + 273.15 K (convert to Kelvin)
- Ideal gas constant (R) = 0.0821 L·atm/(mol·K)

Substituting the values into the equation:

P × 1.04 L = 0.121 moles × 0.0821 L·atm/(mol·K) × (22.1 + 273.15) K

Simplifying the equation:

P = (0.121 × 0.0821 × (22.1 + 273.15)) / 1.04

Calculating the result:

P ≈ 2.205 atm

Therefore, the pressure of carbon dioxide gas in the reaction vessel is approximately 2.205 atmospheres.