Hydrogen diffuses 4 times as rapidly as a certain
gas. What is the density and molecular weight of the
gas when that of Hydrogen is unity?

To find the density and molecular weight of the gas, we can use Graham’s law of effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Since hydrogen diffuses 4 times as rapidly as the other gas, we have .

Using Graham’s law:

where (for hydrogen) and , we can set up the equation:

Squaring both sides gives us:

So, the molecular weight of the gas is 16 g/mol.

To find the density, we can use the formula for density given by , where is the ideal gas constant and is the temperature in Kelvin. Assuming standard conditions, the density of the gas becomes:

Thus, its density is 16 times the density of hydrogen under the same conditions. If we take the density of hydrogen as approximately 0.0899 g/L at STP, the density of the gas is approximately g/L = 1.4384 g/L.