Animated Solution for Chemistry - States of Matter: The volume occupied by 4.75 g of acetylene gas at 50°C and 740 mm Hg pressure is ……L (Rounded off to the nearest integer). [Given, $R=0.0821{\text{ L atm K}}^{-1}{\text{ mol}}^{-1}$]

Imagine a closed container filled with acetylene gas ($C_2{H}_2$). We are given a specific snapshot of its physical state: its mass $w=4.75\text{ g}$, its temperature $T=50^{\circ }\text{C}$, and the pressure it exerts on the walls $P=740\text{ mm Hg}$. Our ultimate goal is to find the exact volume $V$ this gas occupies under these specific conditions.

To connect pressure, volume, temperature, and moles, we use the master key of the gaseous state: the Ideal Gas Equation, $pV=nRT$. But before we can simply plug in the numbers, we must ensure all our units are perfectly aligned with the universal gas constant $R=0.0821{\text{ L atm K}}^{-1}{\text{ mol}}^{-1}$. This is where many students make silly mistakes, so we must proceed with caution.

First, let's fix the temperature. It is given in Celsius, but the gas laws strictly demand the absolute scale, which is Kelvin. So, we add $273$ to $50$, giving us a working temperature of $T=323\text{ K}$.

Next up is pressure. It is given as $740\text{ mm Hg}$. Since our gas constant $R$ uses atmospheres, we must convert this by dividing by standard atmospheric pressure in mm Hg, which is $760$. Thus, $P=\frac{740}{760}\text{ atm}$. Let's keep it as a fraction for now to avoid messy decimals early in our calculation.

Now, we need the number of moles ($n$). Acetylene is $C_2{H}_2$. Two carbon atoms give $24\text{ g/mol}$, and two hydrogen atoms give $2\text{ g/mol}$, making its molar mass $M=26\text{ g/mol}$. Dividing the given mass by the molar mass gives us our moles: $n=\frac{4.75}{26}\text{ mol}$.

We have all our pieces ready. Let's rearrange the ideal gas equation to solve for volume $V$:

Substituting our carefully prepared values, we get this raw expression:

Don't get intimidated by the numbers; it is just basic arithmetic from here. Let's rearrange the fractions to make it easier to compute:

Multiplying the numerators gives us roughly $95715.48$, and the denominator is $19240$. Dividing them, we arrive at a volume of approximately $4.975\text{ L}$.

The question specifically asks us to round off to the nearest integer. Since $4.975$ is incredibly close to $5$, our final answer is simply $5\text{ L}$. A perfect, clean integer.