Question

1. a gas system has pressure, volume and moles of 1.53 atm, 8.190l and 0.612moles, respectively. what is the temperature in k? a) 249k b) 20.5k c) 293k d) 522k

Explanation:

Step1: Recall ideal - gas law

The ideal - gas law is $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the ideal - gas constant ($R=0.0821\ L\cdot atm/(mol\cdot K)$), and $T$ is temperature.
We need to solve for $T$, so we can re - arrange the formula to $T=\frac{PV}{nR}$.

Step2: Substitute given values

Given $P = 1.53\ atm$, $V = 8.190\ L$, $n = 0.612\ moles$, and $R = 0.0821\ L\cdot atm/(mol\cdot K)$.
$T=\frac{1.53\ atm\times8.190\ L}{0.612\ moles\times0.0821\ L\cdot atm/(mol\cdot K)}$.
First, calculate the numerator: $1.53\times8.190 = 12.5307\ L\cdot atm$.
Then, calculate the denominator: $0.612\times0.0821=0.0502452\ L\cdot atm/K$.

Step3: Calculate temperature

$T=\frac{12.5307\ L\cdot atm}{0.0502452\ L\cdot atm/K}\approx249\ K$.

Answer:

A. 249K