Identify the invalid equation.

Q11

Step 1: First law of thermodynamics: $\Delta U = q + w$.

For isothermal process of ideal gas, $\Delta U = 0$ (since $U$ depends only on $T$).

Thus, $q = -w$.

\Delta U = 0

Q12

Step 1: Work for reversible isothermal expansion of ideal gas:

$w = -nRT \ln\left(\frac{V_2}{V_1}\right)$

Step 2: Substitute $n = 1$ mol, $R = 8.314$ J/mol·K, $T = 300$ K, $V_1 = 10$ L, $V_2 = 100$ L.

$nRT = (1)(8.314)(300) = 2494.2$ J

Step 3: $\ln(100/10) = \ln 10 = 2.3026$

Step 4: Simplify:

$w = -2494.2 \times 2.3026 = -5746$ J $= -5.75$ kJ $\approx -5.7$ kJ

-5.7 kJ

Q13

Step 1: Moles of ethane: assume mass $= 60$ g, $M = 30$ g/mol, so $n =