A certain volume of gas S takes 180 secs to diffuse through a porous plug. An equal amount of gas Q takes 240 secs to diffuse the same plug. Calculate the molar mass of gas Q if the molar mass of gas S is 18.​

31.98g/mol

Explanation:

Using Graham's law of diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molecular mass (M). Rate of diffusion = volume/time.

Since both gas S and Q have equal volumes, we can calculate molecular mass of gas Q as follows:

tQ/tS = √mQ /√mS

Where:

tQ = time of diffusion of gas Q

tS = time of diffusion for gas S

mQ = molar mass of gas Q

mS = molar mass of gas S

According to the information provided in this question;

tQ = 240s

tS = 180s

mQ = ?

mS = 18g/mol

Using tQ/tS = √mQ /√mS

240/180 = √mQ / √18

1.333 = √mQ / √18

Square both sides

1.333² = mQ/18

1.78 = mQ/18

mQ = 18 × 1.78

mQ = 31.98g/mol

Molar mass of Q = 31.98g/mol