at what celsius temperature does 0.750 mol of an ideal gas occupy a volume of 35.9 l at 114 kpa?\n______…

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, and $T$ is temperature in Kelvin. First, convert the given values to SI units if necessary. The ideal - gas constant $R=8.314\ J/(mol\cdot K)$. The pressure $P = 114\ kPa=114000\ Pa$, the volume $V = 35.9\ L = 0.0359\ m^{3}$, and $n = 0.750\ mol$.

Step2: Solve for $T$

From $PV=nRT$, we can express $T$ as $T=\frac{PV}{nR}$. Substitute the values: $T=\frac{114000\ Pa\times0.0359\ m^{3}}{0.750\ mol\times8.314\ J/(mol\cdot K)}$. [ \begin{align*} T&=\frac{114000\times0.0359}{0.750\times8.314}\ &=\frac{4092.6}{6.2355}\ &\approx656.338\ K \end{align*} ]

Step3: Convert Kelvin to Celsius

The conversion formula from Kelvin to Celsius is $t=T - 273.15$. So $t=656.338 - 273.15=383.188\approx383$.

Answer:

383