The answer for the given problem is mentioned below.
Explanation:
Given:
Pressure of oxygen ([tex]P_{1}[/tex]) = 980 mm of Hg
Pressure of unknown gas ([tex]P_{2}[/tex]) = 940 mm of Hg
Volume of oxygen ([tex]V_{1}[/tex]) = 400 cm³
To find:
Volume of unknown gas ([tex]V_{2}[/tex])
We know;
According to the ideal gas equation;
P × V = n × R × T
where,
P represents the pressure of the gas
V represents the volume of the gas
n represents the no of moles of the gas
R represents the universal gas constant
T represents the temperature of the gas
From the above equation;
P×V = constant
P ∝ [tex]\frac{1}{V}[/tex]
Therefore;
[tex]\frac{P_{1} }{P_{2} }[/tex] = [tex]\frac{V_{2} }{V_{1} }[/tex]
where;
[tex]\frac{980}{940}[/tex] = [tex]\frac{V_{2} }{400}[/tex]
[tex]V_{2}[/tex] = [tex]\frac{980 * 400}{940}[/tex]
[tex]V_{2}[/tex] = 417 cm³
Therefore volume of the gas is 417 cm³.
