Question
Density of a gas is found to be $5.46 \mathrm{~g} / \mathrm{dm}^3$ at $27^{\circ} \mathrm{C}$ at 2 bar pressure. What will be its density at STP?
✓
Answer
Given,
$\mathrm{d}_1=5.46 \mathrm{~g} / \mathrm{dm}^3$
$\mathrm{p}_1=2 \mathrm{bar}$
$\mathrm{T}_1=27^{\circ} \mathrm{C}=(27+273) \mathrm{K}=300 \mathrm{~K}$
$\mathrm{p}_2=1 \mathrm{bar}$
$\mathrm{T}_2=273 \mathrm{~K}$
$\mathrm{d}_2=?$
The density $\left(\mathrm{d}_2\right)$ of the gas at STP can be calculated using the equation,
$\text{d}=\frac{\text{Mp}}{\text{RT}}$
$\therefore\ \frac{\text{d}_1}{\text{d}_2}=\frac{\frac{\text{Mp}_1}{\text{RT}_1}}{\frac{\text{Mp}_2}{\text{RT}_2}}$
$\Rightarrow\ \frac{\text{d}_1}{\text{d}_2}=\frac{\text{p}_1\text{T}_2}{\text{p}_2\text{T}_1}$
$\Rightarrow\ \text{d}_2=\frac{\text{p}_2\text{T}_1\text{d}_1}{\text{p}_1\text{T}_2}$
$=\frac{1\times300\times5.46}{2\times273}$
$=3\text{g dm}^{-3}$
Hence, the density of the gas at STP will be $3 \mathrm{g} \mathrm{~dm}^{-3}$.
$\mathrm{d}_1=5.46 \mathrm{~g} / \mathrm{dm}^3$
$\mathrm{p}_1=2 \mathrm{bar}$
$\mathrm{T}_1=27^{\circ} \mathrm{C}=(27+273) \mathrm{K}=300 \mathrm{~K}$
$\mathrm{p}_2=1 \mathrm{bar}$
$\mathrm{T}_2=273 \mathrm{~K}$
$\mathrm{d}_2=?$
The density $\left(\mathrm{d}_2\right)$ of the gas at STP can be calculated using the equation,
$\text{d}=\frac{\text{Mp}}{\text{RT}}$
$\therefore\ \frac{\text{d}_1}{\text{d}_2}=\frac{\frac{\text{Mp}_1}{\text{RT}_1}}{\frac{\text{Mp}_2}{\text{RT}_2}}$
$\Rightarrow\ \frac{\text{d}_1}{\text{d}_2}=\frac{\text{p}_1\text{T}_2}{\text{p}_2\text{T}_1}$
$\Rightarrow\ \text{d}_2=\frac{\text{p}_2\text{T}_1\text{d}_1}{\text{p}_1\text{T}_2}$
$=\frac{1\times300\times5.46}{2\times273}$
$=3\text{g dm}^{-3}$
Hence, the density of the gas at STP will be $3 \mathrm{g} \mathrm{~dm}^{-3}$.
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