Question

if the pressure exerted by a gas at 25 degrees c in a volume of 0.044 l is 3.81 atm, how many moles of gas are present?
.0069 mol
9.887 mol

Explanation:

Step1: Convert temperature to Kelvin

The ideal gas law is \(PV = nRT\). First, convert \(T = 25^{\circ}C\) to Kelvin. \(T=(25 + 273.15)K=298.15K\). The gas constant \(R = 0.0821\frac{L\cdot atm}{mol\cdot K}\), \(P = 3.81atm\), \(V=0.044L\).

Step2: Rearrange the ideal - gas law for \(n\)

From \(PV=nRT\), we can solve for \(n\) as \(n=\frac{PV}{RT}\).
Substitute the values: \(n=\frac{3.81\times0.044}{0.0821\times298.15}\).
Calculate the numerator: \(3.81\times0.044 = 0.16764\).
Calculate the denominator: \(0.0821\times298.15\approx24.488\).
Then \(n=\frac{0.16764}{24.488}\approx0.0069mol\).

Answer:

\(0.0069mol\)