A vessel contains a mixtrue consisting of `m_(1) = 7g` of nitrogen `M_(1) = 28 and m_(2) = 11 g` of carbon dioxide `(M_(2) 44)` at temperature` T = 300 K` and pressure `p_(0) = 1` atm. Find the density of the mixture.

Explanation

Let V be the volume of the vessel. Then `rho_(mis)=(m_(1) + m_(2))/(V)`
Let `p_(1) and p_(2)` be the partial pressure
Then `p_(1)V = (m_(1))/(M_(1))RT` and `P_(2)V = (m_(2))/(M_(2))RT, p_(0) = p_(1) + p_(2)`
`therefore " "p_(0) = (m_(1)/M_(1) + m_(2)/M_(2))(RT)/(T)`
`therefore " "rho_(mix)=((m_(1) + m_(2))M_(1)M_(2))/(M_(1)M_(2) + m_(2)M_(1))xx(p_(0))/(RT)`
`=((7+11)xx28xx44xx10^(-3))/(7xx44+11xx28) xx (10^(5))/(8.3xx300)`
`=1.446 kg m^-3 = 1.446` per litre