Question

A gas made up of atoms escapes through a pinhole times as fast as gas. Write the chemical formula of the gas.

Answer 1

A gas made up of atoms escapes through a pinhole 0.225times as fast as gas. Write the chemical formula of the gas.

Answer:

Explanation:

To solve this problem, we must apply Graham's law of diffusion. This law states that "the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molecular mass at constant temperature and pressure".

Mathematically;

                 $\frac{r_{1} }{r_{2} } = \frac{\sqrt{m_{2} } }{\sqrt{m_{1} } }$

r₁ is the rate of diffusion of gas 1

r₂ is the rate of diffusion of gas 2

m₁ is the molar mass of gas 1

m₂ is the molar mass of gas 2

let gas 2 be the given H₂;

   molar mass of H₂ = 2 x 1 = 2gmol⁻¹

rate of diffusion is 0.225;

  i .e r1/r2 = 0.225

          0.225 = √2  /  √ m₁

           0.225 = 1.414 / √ m₁

           

       √ m₁  = 6.3

           m₁  = 6.3²  = 39.5g/mol

The gas is likely Argon since argon has similar molecular mass