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-An ideal gas initially at 50ºC and pressure P₁ = 100 kPa occupies a volume V₁ = 3 L.It undergoes a quasi-static,isothermal expansion until its pressure is reduced to 50 kPa.How much work was done by the gas during this process? R = 8.314 J/mol·K = 8.206 L·atm/mol·K.

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-An ideal gas initially at 50ºC and pressure P₁ = 100 kPa occupies a volume V₁ = 3 L.It undergoes a quasi-static,isothermal expansion until its pressure is reduced to 50 kPa.How much work was done by the gas during this process? R = 8.314 J/mol·K = 8.206 L·atm/mol·K.

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The work done by an ideal gas during a quasi-static isothermal expansion can be calculated using the formula $W = nRT \ln\left(\frac{V_f}{V_i}\right)$, where $n$ is the number of moles of gas, $R$ is the ideal gas constant, $T$ is the temperature in Kelvin, $V_f$ is the final volume, and $V_i$ is the initial volume. Since the process is isothermal, $T$ remains constant, and the pressure-volume relationship $P_iV_i = P_fV_f$ can be used to find the ratio of final to initial volumes. Given that $P_i = 100$ kPa, $P_f = 50$ kPa, and $V_i = 3$ L, we find $V_f = 2V_i = 6$ L because the pressure is halved. However, to calculate work, we need to use the appropriate value of $R$. Since the pressures are given in kPa and volumes in L, we should convert $R$ to a compatible unit. The closest match is $8.206$ L·atm/mol·K, but we also need to convert the pressure from kPa to atm (1 atm = 101.325 kPa). The calculation of work does not directly require converting $R$ because we can use the pressures in kPa and volumes in L directly if we adjust $R$ accordingly. The key point is that the work done is dependent on the logarithm of the volume ratio, which is the same regardless of the units of $R$, as long as they are consistent with the units of pressure and volume used in the calculation. The correct calculation involves using the given pressures and volumes with the natural logarithm of the volume ratio. The mistake in the explanation was suggesting a need to convert $R$ or pressures for the calculation, which might imply unnecessary steps. The correct approach is to use the formula for work with the given or appropriately converted units for consistency, focusing on the volume ratio and the initial conditions to find the work done during the expansion.

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