Question

quiz - gas laws
questions

1. a canister filled with 3.75g of argon gas has a fixed volume of 420ml. if this canister is kept at a temperature of 22°c, the pressure inside the canister will be ____ kpa.

your answer:

Explanation:

Step1: Calculate the number of moles of argon

The molar mass of argon ($Ar$) is $M = 39.95\ g/mol$. The number of moles $n$ is calculated by the formula $n=\frac{m}{M}$, where $m = 3.75\ g$. So $n=\frac{3.75\ g}{39.95\ g/mol}\approx0.0939\ mol$.

Step2: Convert temperature to Kelvin

The temperature $T=22^{\circ}C$. To convert to Kelvin, use $T(K)=T(^{\circ}C)+ 273.15$. So $T = 22 + 273.15=295.15\ K$.

Step3: Convert volume to SI - unit (cubic - meters)

The volume $V = 420\ mL=420\times10^{- 6}\ m^{3}$.

Step4: Apply the ideal gas law

The ideal gas law is $PV = nRT$, where $R = 8.314\ J/(mol\cdot K)$. We want to find $P$, so $P=\frac{nRT}{V}$. Substitute $n = 0.0939\ mol$, $R = 8.314\ J/(mol\cdot K)$, $T = 295.15\ K$ and $V=420\times10^{-6}\ m^{3}$ into the formula.
$P=\frac{0.0939\ mol\times8.314\ J/(mol\cdot K)\times295.15\ K}{420\times10^{-6}\ m^{3}}$
$P=\frac{0.0939\times8.314\times295.15}{420\times10^{-6}}\ Pa$
$P\approx547953\ Pa$.
To convert to $kPa$, divide by $1000$. So $P\approx548\ kPa$.

Answer:

548