Question

data:
cylinder volume = 2500 cc
pressure after the throttle valve = 0.5 bar
air temperature = 27 °c (300 k)
mass 1 liter air = 1.29 g at 0 °c.

what is the mass of the air drawn in?
1.13 g
ok

Explanation:

Step1: Use the ideal gas law relation for density

The density of air at \(0^{\circ}C\) (\(T_1 = 273\ K\)) and \(P_1= 1\ bar\) is \(
ho_1=\frac{1.29}{1}\ g/L\).
For an ideal gas \(PV = nRT\) and \(
ho=\frac{m}{V}=\frac{P}{RT}M\) (where \(M\) is molar mass). So \(\frac{
ho_2}{
ho_1}=\frac{P_2T_1}{P_1T_2}\)

Step2: Substitute the given values

Given \(P_1 = 1\ bar\), \(T_1=273\ K\), \(P_2 = 0.5\ bar\), \(T_2=(27 + 273)\ K=300\ K\)
\(
ho_2=
ho_1\times\frac{P_2T_1}{P_1T_2}\)
\(
ho_2 = 1.29\times\frac{0.5\times273}{1\times300}\ g/L\)
\(
ho_2=1.29\times\frac{136.5}{300}\ g/L\)
\(
ho_2 = 1.29\times0.455\ g/L\)
\(
ho_2=0.58695\ g/L\)

Step3: Calculate the mass of air

Cylinder volume \(V = 2500\ cc=2.5\ L\)
Mass \(m=
ho_2\times V\)
\(m=0.58695\times2.5\ g\)
\(m = 1.467375\ g\approx1.47\ g\)

Answer:

\(1.47\ g\)