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: Understanding the Concept:
The ideal gas equation connects pressure, volume, amount of gas and temperature. Since the question gives the product \(RT\) directly, no separate temperature is needed.

Step 2: Key Formula:
\[ PV = nRT \Rightarrow n = \frac{PV}{RT} \]

Step 3: Detailed Explanation:
Given \(P = 1.104 \times 10^5\) N m\(^{-2}\), \(V = 4 \times 10^{-3}\) m\(^3\) and \(RT = 2208\) J mol\(^{-1}\).
\[ PV = 1.104 \times 10^5 \times 4 \times 10^{-3} = 441.6 \text{ J} \]
\[ n = \frac{441.6}{2208} = 0.2 \text{ mol} \]
Units check: N m\(^{-2}\) times m\(^3\) gives N m = J, and J divided by J mol\(^{-1}\) gives mol.

Step 4: Why the other options are wrong.
Values 0.1, 0.3 and 0.4 mol would need \(PV\) of 220.8, 662.4 and 883.2 J, which do not match the product of the given pressure and volume.

Final Answer:
The sample contains \(0.2\) mole of \(\text{CO}_2\), option (B). \[ \boxed{0.2 \text{ mol}} \]