Question

: A gas is found to have a formula${{\left (CO \right)}_{x}}$. If its vapor density is $70$then the value of x is:
A.$2\cdot 5$
B.$3$
C.$5$$70$
D.$6$

Answer 1

Hint:The molecular weight of a gas is double times its vapor density. The value of vapor density is given so we can find its molecular weight. In the given formula, the unknown is x but we can find the weight of CO. Simply divide the total weight found from vapor density to the weight of CO to get the value of x.
Formula Used:
 Molecular weight$=2\times $vapor density$=70$

Complete step by step answer:
Given, vapor density $=70$
So, using the above formula, Molecular weight$=2\times $vapor density$=70$
 We get molecular weight for the given gas $\begin {align}
  & =\, 2\times 70 \\
 & =\, 140 \\
\end{align}$
Molecular mass for CO $\begin {align}
  & =\, 12\, +\, 16 \\
 & =\, 28 \\
\end{align}$
So now according to the given formula of gas${{\left (CO \right)}_{x}}$, CO is multiplied by x to get the total molecular weight. So, $\begin {align}
  & 28\times x\, =\, 140 \\
 & \Rightarrow \, x\, =\,\dfrac{140}{28} \\
 & \,\,x\,=\,5 \\
\end{align}$

So the correct choice is (C).

Additional Information:
Vapor density is defined as the ratio of molar mass of gas to the molar mass of hydrogen molecule. This is the reason why in the above used formula vapor density was multiplied by $2$ in order to get the molar mass of gas because the molar mass of hydrogen molecule is $2$. Many times vapor density is defined with respect to air instead of hydrogen; ex- acetone has vapor density $2$ with respect to air which means its vapors are double times heavier than air. So, vapor density can be used to determine whether the given gas will rise or sink in air. If the vapor density of a gas is greater than one it means the gas is heavier than air if it is less than one than it is lighter than air. So we can say that vapor density tells us about the relative weight of the given gas with respect to hydrogen or air.

Note:
The molar mass for can be simply found by adding the molar masses of its constituent elements. The molar mass or atomic mass of an element is found by multiplying its atomic number by two if the atomic number is even and by adding one to the previous result if the atomic number is odd. One needs a thorough study of the periodic table in order to remember the atomic number of elements and their corresponding atomic masses.