What is the pressure exerted by 4.5m$^3$ of gas at 17ºC in a cylinder if the number of moles is 8.3 moles? (R = 8.31 JK$^{-1}$mol$^{-1}$)

1. Analyze the Question

We are asked to find the pressure ($P$) of a gas given its volume ($V$), temperature ($T$), and the number of moles ($n$). We are also provided with the universal gas constant ($R$).

2. Explain the Concept

This problem requires the Ideal Gas Law equation:

Where:

• $P$ = Pressure (in Pascals, Pa)
• $V$ = Volume (in cubic meters, m³)
• $n$ = Number of moles (mol)
• $R$ = Universal gas constant (8.31 JK⁻¹mol⁻¹)
• $T$ = Absolute temperature (in Kelvin, K)

Important Note: In physics calculations involving gas laws, temperature must always be in Kelvin. To convert Celsius to Kelvin, use the formula: $T(K) = T(^\circ C) + 273$.

3. Show the Solution

Step 1: Convert temperature to Kelvin

Step 2: Rearrange the Ideal Gas Law to solve for $P$

Step 3: Substitute the given values into the formula

• $n = 8.3 \, \text{mol}$
• $R = 8.31 \, \text{JK}^{-1}\text{mol}^{-1}$
• $T = 290 \, K$
• $V = 4.5 \, \text{m}^3$

Step 4: Calculate the numerator

Step 5: Divide by the volume

Rounding to the nearest whole number, we get 4445 Pa.

4. Identify the Answer

Comparing our result to the options provided, the correct value is 4445 Pa. This matches option D.

5. Exam Tip

Always check your units before starting! JAMB examiners love to give temperatures in Celsius to see if you remember to add 273. Also, ensure your volume is in m³; if it were given in cm³, you would need to convert it by multiplying by $10^{-6}$.