A vessel contains a mixture of `7 g` of nitrogen and `11 g` of carbon dioxide at temperature `T = 300 K`. If the pressure of the mixutre is 1 atm `(1 xx 10^(5) N//m^(2))`, its density is (gas constant `R = 25//3 J//mol K)`

Options

A. `0.72 kg//m^(3)`
B. `1.44 kg//m^(3)`
C. `2.88 kg//m^(3)`
D. `5.16 kg//m^(3)`

Answer

B

Explanation

b. Density or mixture, `rho_(mix) = (PM_(mix))/(RT)`
Mass or nitrogen gas, `m_(N) = 7 g = 7 xx 10^(-3) kg`
Mass of carbon dioxide, `m_(C0_(2)) = 11 g = 11 xx 10^(-3) kg`
Molecular weight of nitrogen gas, `M_(N) = 28 xx 10^(-3) kg`
Molecular weight of carbon dioxide, `M_(CO_(2)) = 44 xx 10^(-3) kg`
`M_(mix) = (n_(N) M_(N))/(n_(N) + n_(CO_(2))) = ((m_(N))/(M_(N)) M_(N) + (m_(CO_(2)))/(M_(CO_(2))) M_(CO_(2)))/((m_(N))/(M_(N)) + (m_(CO_(2)))/(M_(CO_(2)))`
` = (m_(N) + m_(CO_(2)))/((m_(N))/(M_(N)) + (m_(CO_(2)))/(M_(CO_(2)))) = ((7 + 11) xx 10^(-3))/(((7)/(28) + (11)/(44)))`
` = (18 xx 10^(-3))/((1)/(4) + (1)/(4)) = 36 xx 10^(-3) kg`
`rho = ((1 xx 10^(5))(36 xx 10^(-3)))/((25)/(3) xx 300) = 1.44 kg//m^(3)`