Import Question JSON

$\text{Hint: Apply the First Law of Thermodynamics}$ $\text{Step 1: Identify the given information}$ $\text{• 1 g of H}_2 \text{ gas at S.T.P. (Standard Temperature and Pressure)}$ $\text{• The gas expands to twice its initial volume}$ $\text{• S.T.P. conditions: 273 K (0°C) and 1 atm pressure}$ $\text{Step 2: Calculate the initial and final volumes}$ $V_1 \text{ (volume of 1 g H}_2\text{) = 11.2 L at STP}$ $\text{Since the gas expands to twice its initial volume:}$ $V_2 \text{ (final volume) = 2 } \times V_1 = 2 \times 11.2 \text{ L} = 22.4 \text{ L}$ $\text{Step 3: Calculate the work done using Method 1 (pressure-volume work)}$ $\text{For an expansion against a constant external pressure, the work is:}$ $W = -P_{\text{ext}}\Delta V$ $\text{Where:}$ $\text{• } P_{\text{ext}} \text{ is the external pressure (1 atm at STP)}$ $\text{• } \Delta V \text{ is the change in volume } (V_2 - V_1)$ $\Delta V = V_2 - V_1 = 22.4 \text{ L} - 11.2 \text{ L} = 11.2 \text{ L}$ $W = -P_{\text{ext}}\Delta V = -1 \text{ atm} \times 11.2 \text{ L} = -11.2 \text{ L atm}$ $\text{The negative sign indicates that the system does work on the surroundings.}$ $\text{However, the question asks for the magnitude of work, which is 11.2 L atm.}$ $\text{Step 4: Verify with Method 2 (using gas laws)}$ $\text{We can also calculate the work using the relationship:}$ $W = \Delta (nRT)$ $\text{For 1 g of H}_2\text{, the number of moles is:}$ $n = \frac{\text{mass}}{\text{molar mass}} = \frac{1 \text{ g}}{2 \text{ g/mol}} = 0.5 \text{ mol}$ $\text{For an isothermal process at STP (T = 273 K):}$ $W = 0.5 \text{ mol} \times 2 \text{ cal/(mol·K)} \times 273 \text{ K} = 273 \text{ cal}$ $\text{Converting to L·atm using the conversion factor 1 L·atm = 24.2 cal:}$ $W = \frac{273 \text{ cal}}{24.2 \text{ cal/L·atm}} = 11.2 \text{ L·atm}$ $\text{Therefore, the work done during the expansion is 11.2 L atm.}$