Answer:
31.98g/mol
Step-by-step 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