If a mixture of $28$g of nitrogen, $4$g of hydrogen and $8$g of helium is contained in a vessel at temperature $400$K and pressure $8.3\times10^5$Pa, the density of the mixture will be:-

Calculate the total mass of the mixture by summing the given masses of nitrogen, hydrogen, and helium to get 40 grams or 0.04 kilograms. Using the ideal gas law PV = nRT with the given pressure of 8.3 x 10^5 Pascals, the total moles of 3, the temperature of 400 Kelvin, and the gas constant R=8.3, the volume of the vessel is found to be 0.032 cubic meters. The density of the mixture is then mass divided by volume, which is 0.04 kg / 0.032 m^3, equaling 1.25 kg/m^3.

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