Calculate the final temperature when 2.50 kJ of energy is transferred as heat to 1.50 mol N₂ at 298 K and 1 atm at constant volume.

Question

Quizplus · Accepted Answer

The final temperature can be calculated using the formula $q = nC_{v}\Delta T$, where $q$ is the heat transferred, $n$ is the number of moles, $C_{v}$ is the molar heat capacity at constant volume, and $\Delta T$ is the change in temperature. Given that $q = 2.50 \, \text{kJ}$, $n = 1.50 \, \text{mol}$, and assuming a typical molar heat capacity for a diatomic molecule (since N₂ is not a standard chemical formula, we'll assume a generic value) of about $20.8 \, \text{J/mol}\cdot\text{K}$, we can solve for $\Delta T$. Rearranging the formula gives $\Delta T = \frac{q}{nC_{v}}$. Plugging in the values (and converting $q$ to J by multiplying by 1000), we get $\Delta T = \frac{2500 \, \text{J}}{1.50 \, \text{mol} \times 20.8 \, \text{J/mol}\cdot\text{K}}$, which calculates to a change in temperature. Adding this change to the initial temperature of 298 K gives a final temperature in Kelvin, which can then be converted to °C. The closest match to the calculated value will be choice E, 105°C, based on typical values for $C_{v}$ and the given conditions.

Calculate the Final Temperature When 2 ∘\circ∘ C B) 145 ∘\circ∘ C C) 159

Calculate the Final Temperature When 2 $\circ$ C
B) 145^$\circ$C
C) 159