Question

A 5.2 L closed container contains some water and N$_2$(g) at 29 $^\circ$C. The total pressure of the system and water tension are 1 atm and 0.04 atm, respectively. Upon electrolysing the liquid water inside completely, the final pressure of system was at 2 atm. What is number of moles of water that was present inside the container?

• A. $\frac{3.46}{RT}$
• B. $\frac{5.2}{RT}$
• C. $\frac{10.4}{RT}$
• D. $\frac{0.208}{RT}$
• E. $\frac{8.0}{RT}$

Hint:

Aqueous tension is the pressure exerted by water vapor in equilibrium with liquid water; it is a partial pressure.

Answer 1

The Correct Option is D

Concept: Dalton's Law states that total pressure is the sum of partial pressures of gases in the mixture. Water tension refers to the vapor pressure of water.

Step 1: {Determine the initial partial pressure of Nitrogen.} $P_{total} = P_{N_2} + P_{H_2O(vap)}$. $1.0 \text{ atm} = P_{N_2} + 0.04 \text{ atm}$. $$P_{N_2} = 1.0 - 0.04$$ $$P_{N_2} = 0.96 \text{ atm}$$

Step 2: {Determine the partial pressure of water vapor separately.} The "moles of water" in this context refers to the moles of vapor present inside the volume ($V = 5.2$ L) at temperature $T$. Using the ideal gas equation: $PV = nRT$. $0.04 \times 5.2 = n_{water} \times RT$.

Step 3: {Solve for the number of moles.} Rearranging the equation for $n_{water}$: $$n_{water} = \frac{0.04 \times 5.2}{RT}$$ $$0.04 \times 5.2 = 0.208$$ $$n_{water} = \frac{0.208}{RT}$$