Question

Find the number of moles of \(\text{CO}_2\) present in a sample occuping \(4\times 10^{-3}\,\text{m}^3\) at \(1.104\times 10^5\,\text{Nm}^{-2}\) pressure (\(R\times T = 2208 \text{J mol}^{-1}\))

• A. \(0.1\) mole
• B. \(0.2\) mole
• C. \(0.3\) mole
• D. \(0.4\) mole

Hint:

Use PV = nRT directly with the given values of P, V and RT.

Answer 1

The Correct Option is B

Step 1: Plan:
Rearrange the ideal gas law to get moles, then plug in numbers using SI units throughout.

Step 2: Compute the numerator:
$P \times V$: $1.104 \times 4 = 4.416$, and the powers of ten $10^5 \times 10^{-3} = 10^2$. So $PV = 441.6$ J.

Step 3: Divide by RT:
$n = 441.6 / 2208$. Since $2208 = 441.6 \times 5$, the ratio is $1/5 = 0.2$ mol.

Step 4: Sanity check:
At about 1.1 bar and near 265 K, 4 litres of gas is a fraction of a mole, so 0.2 mol is reasonable.

Final Answer:
There are 0.2 mol of gas, option (B). \[ \boxed{0.2 \text{ mol}} \]