what volume does 4.53 moles of hydrogen at 1.78 atm and 301 k occupy? ? l

Explanation:

Step1: Identify the ideal - gas law formula

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 ($R=0.0821\ \frac{L\cdot atm}{mol\cdot K}$), and $T$ is temperature in Kelvin. We want to solve for $V$, so we can rewrite the formula as $V=\frac{nRT}{P}$.

Step2: Substitute the given values

We are given that $n = 4.53\ mol$, $P = 1.78\ atm$, $T = 301\ K$, and $R=0.0821\ \frac{L\cdot atm}{mol\cdot K}$. $V=\frac{4.53\ mol\times0.0821\ \frac{L\cdot atm}{mol\cdot K}\times301\ K}{1.78\ atm}$

Step3: Calculate the volume

First, calculate the numerator: $4.53\times0.0821\times301 = 4.53\times24.7121=112.945813$. Then, divide by the denominator: $V=\frac{112.945813}{1.78}\approx63.4\ L$.

Answer:

$63.4$