Question

A mixture of CO and CO$_2$ has vapour density 20 at STP. 100 g of this mixture contains ____ mole of CO

• A. 0.4
• B. 0.2
• C. 0.625
• D. 0.375

Hint:

For gas mixture: Average molar mass = total mass / total moles, and V.D. = \(M/2\).

Answer 1

The Correct Option is C

Step 1: Vapour density 20 ⇒ molar mass of mixture \[ M_{\text{mix}} = 2 \times \text{V.D.} = 40 \text{ g mol}^{-1}. \]
Step 2: Let moles of CO = \(x\), moles of CO$_2$ = \(y\). Total moles: \[ x+y=\frac{100}{40}=2.5 \text{ mol}. \quad\cdots(1) \]
Step 3: Mass equation using molar masses (\(M_{\text{CO}}=28\), \(M_{\text{CO$_2$}}=44\)) \[ 28x+44y=100. \quad\cdots(2) \]
Step 4: From (1), \(y=2.5-x\). Substitute in (2): \[ 28x+44(2.5-x)=100 \] \[ 28x+110-44x=100 \] \[ -16x=-10 \] \[ x=0.625 \text{ mol}. \] Hence the mixture contains 0.625 mole of CO.