Final answer:
The student's task is to use the ideal gas law to find the number of moles of an ideal gas and calculate the work done during an isothermal, reversible expansion. The moles of gas can be calculated by rearranging the ideal gas equation PV = nRT and the work is calculated using the formula w = -nRT · ln(V2/V1).
Step-by-step explanation:
The student's question concerns a reversible isothermal expansion of an ideal gas using the ideal gas law to calculate the number of moles of gas and the work done during the expansion, w. First, we can use the initial conditions provided (volume, temperature, and pressure) to find the number of moles of the ideal gas using the formula PV = nRT, where P is the pressure, V is the volume, R is the ideal gas constant (0.0821 L·atm/K·mol), and T is the temperature. Substituting the given values, we have:
2.47 atm × 3.67 L = n × 0.0821 L·atm/K·mol × 298 K
Solving for n, we get:
n = moles of gas = (2.47 atm × 3.67 L) / (0.0821 L·atm/K·mol × 298 K)
To calculate the work done, w, in an isothermal, reversible expansion, we use the equation w = -nRT · ln(V2/V1), where V1 is the initial volume and V2 is the final volume. Given that the temperature is constant (isothermal process), we can solve for w using the previously calculated n value:
w = -n × R × T · ln(8.54 L / 3.67 L).
Substitute the known values to find the work done by the gas during the expansion.