Question

In a flask, the weight ratio of \[C{H_4}(g)\] and \[S{O_2}(g)\] at \[298{\text{ }}K\] and $1$ bar is \[1:2\] . The ratio of the number of molecules of \[S{O_2}(g)\] and \[C{H_4}(g)\] is:
A. $1:4$
B. $4:1$
C. $1:2$
D. $2:1$

Answer 1

Hint: In the given question firstly we have to first take the ratio that is given regarding the weights of the gases. Then we can just pick the important details from the question and then use the molecular formula to convert the entire scenario of molecular weight into the moles and then find the ratio of the gases in terms of moles.

Complete step by step answer:
Here first we have to take out the points that were mentioned in the question itself :
The weight ratio of \[C{H_4}(g)\] and \[S{O_2}(g)\] in the question is : \[1:2\]
The temperature of the given system is : \[298{\text{ }}K\]
The pressure of the given system is : $1$ bar
Now we have to perform the step by step process in order to have the answers to the given question from the given data.
Step $1$ : We have to get the number of moles of the given gases by the help of the ratio of their weights using their molecular weight.
Molecular weight of \[C{H_4}(g)\] : $16g$
Molecular weight of \[S{O_2}(g)\] : $64g$
So we have to use the given formula regarding the mole ratio:
\[ = \dfrac{{{w_1}}}{{{M_1}}} \times \dfrac{{{M_2}}}{{{w_2}}}\]
Where the ${w_1}\& {w_2}$ are the weights and the ${M_1}\& {M_2}$ are the molar weights
Step $2$ : Now we just have to put the values and then solve in order to find the answer :
\[
= \dfrac{{{w_1}}}{{{M_1}}} \times \dfrac{{{M_2}}}{{{w_2}}} \\
= \dfrac{2}{{64}} \times \dfrac{{16}}{1} \\
= \dfrac{1}{2} \\
 \]
Therefore we can say that the right ratio for the number of molecules of \[S{O_2}(g)\] and \[C{H_4}(g)\] is: $1:2$

So, the correct answer is Option C.

Note: In the field of physical chemistry, the mole ratio can be defined as a conversion factor that relates the amounts in moles of any two substances in a chemical reaction. Therefore we can say that the numbers in a conversion factor will come from the coefficients of the balanced chemical equation.