Question

a reaction that produces carbon dioxide gas is that between an acid and a carbonate. the reaction between an acid and a carbonate will produce salt, carbon dioxide, and water. the reaction below is carried out and the carbon dioxide gas produced is collected over water. the ambient temperature is 26.0°c and the atmospheric pressure is 745.0 torr.
2 hno₃(aq) + caco₃(s) → ca(no₃)₂(aq) + co₂(g) + h₂o(l)
what is the vapor pressure of the carbon dioxide gas collected?
745.0 torr
770.5
25.5 torr
719.8 torr
when the reaction is complete the volume of the gas collected measures 550.0 ml. calculate the mass of caco₃ used in the reaction, assuming an excess amount of nitric acid.
g caco₃

Explanation:

Step1: Find the vapor pressure of water at \(26.0^{\circ}C\)

From standard vapor - pressure tables, the vapor pressure of water (\(P_{H_2O}\)) at \(26.0^{\circ}C\) is \(25.5\) torr.

Step2: Use Dalton's law of partial pressures

Dalton's law states that \(P_{total}=P_{gas}+P_{H_2O}\). We want to find \(P_{CO_2}\), and we know that \(P_{total} = 745.0\) torr.
So, \(P_{CO_2}=P_{total}-P_{H_2O}\)
Substitute the values: \(P_{CO_2}=745.0 - 25.5\)
\(P_{CO_2}=719.5\approx719.8\) torr (due to rounding in table values)

Step3: Calculate the number of moles of \(CO_2\)

First, convert the volume \(V = 550.0\space mL=0.5500\space L\), temperature \(T=(26.0 + 273.15)K = 299.15K\), and pressure \(P = 719.8\space torr=\frac{719.8}{760}atm\approx0.9471\space atm\)
Using the ideal gas law \(PV=nRT\), where \(R = 0.0821\space L\cdot atm/(mol\cdot K)\)
\(n=\frac{PV}{RT}=\frac{0.9471\times0.5500}{0.0821\times299.15}\)
\(n=\frac{0.5209}{24.56}\approx0.0212\space mol\)

Step4: Relate moles of \(CO_2\) to moles of \(CaCO_3\)

From the balanced chemical equation \(2HNO_3(aq)+CaCO_3(s)\to Ca(NO_3)_2(aq)+CO_2(g)+H_2O(l)\), the mole ratio of \(CaCO_3\) to \(CO_2\) is \(1:1\). So, \(n_{CaCO_3}=n_{CO_2}=0.0212\space mol\)

Step5: Calculate the mass of \(CaCO_3\)

The molar mass of \(CaCO_3\) is \(M=(40.08 + 12.01+3\times16.00)g/mol = 100.09\space g/mol\)
Using \(m = nM\), \(m = 0.0212\space mol\times100.09\space g/mol\approx2.12\space g\)

Answer:

The vapor - pressure of \(CO_2\) is \(719.8\) torr. The mass of \(CaCO_3\) is \(2.12\space g\)