Question

A certain gaseous mixture contains methane and sulphur dioxide in ratio of 1:8 by mass. The ratio of the number of molecules is :-​

Answer 1

Answer: The ratio of number of molecules of methane is to sulfur dioxide is 1 : 2.

Explanation:

We are given:

Ratio of methane : sulfur dioxide by mass = 1 : 8

Mathematically,

$\frac{M_{CH_4}}{M_{SO_2}}=\frac{1}{8}$

To calculate the number of molecules, we use the equation:

$N_{CH_4}=n_{CH_4}\times N_A=\frac{M_{CH_4}}{M.M_{CH_4}}\times N_A$     .....(1)

where,

$M_{CH_4}$ = given mass of methane

$M.M_{CH_4}$ = molar mass of methane

$N_A$ = Avogadro's number

Similarly,

$N_{SO_2}=n_{SO_2}\times N_A=\frac{M_{SO_2}}{M.M_{SO_2}}\times N_A$        .....(2)

Molar mass of methane = 16 g/mol

Molar mass of sulfur dioxide = 64 g/mol

Taking ratio of equation 1 and 2, we get:

$\frac{N_{CH_4}}{N_{SO_2}}=\left(\frac{\frac{M_{CH_4}}{M.M_{CH_4}}\times N_A}{\frac{M_{SO_2}}{M.M_{SO_2}}\times N_A}\right)\\\\\frac{N_{CH_4}}{N_{SO_2}}=\frac{M_{CH_4}\times N_A}{M.M_{CH_4}}\times \frac{M.M._{SO_2}}{M_{SO_2}\times N_A}\\\\\frac{N_{CH_4}}{N_{SO_2}}=\frac{M_{CH_4}}{M_{SO_2}}\times \frac{M.M_{SO_2}}{M.M_{CH_4}}\\\\\frac{N_{CH_4}}{N_{SO_2}}=\frac{1}{8}\times \frac{64}{16}\\\\\frac{N_{CH_4}}{N_{SO_2}}=\frac{1}{2}$

Hence, the ratio of number of molecules of methane is to sulfur dioxide is 1 : 2.

Answer 2

Answer:

molar mass of methane(CH4) = 16g/mol

molar mass of sulphur do oxide(SO2) =64g/mol

ratio =1 :8

1/8×64/16 =1/2

Ans =1 :2