The volume occupied by 1 mole of an ideal gas at a temperature of 13$^0$C and a pressure of 1.58 atm is  [ R = 0.082 atm dm$^3$ K$^{-1}$mol$^{-1}$ ]

To solve this problem, we use the Ideal Gas Law equation, which relates pressure, volume, temperature, and the number of moles of a gas.

1. Analyze the Question

• Number of moles ($n$) = 1 mol
• Temperature ($T$) = 13°C
• Pressure ($P$) = 1.58 atm
• Gas constant ($R$) = 0.082 atm dm$^3$ K$^{-1}$mol$^{-1}$
• We need to find the Volume ($V$).

2. Explain the Concept

The Ideal Gas Law is expressed as:

Before we plug in the values, we must ensure the temperature is in Kelvin (K), as the gas constant $R$ uses Kelvin.

• $T(K) = T(°C) + 273$
• $T = 13 + 273 = 286 \text{ K}$

3. Show the Solution

Rearrange the formula to solve for $V$:

Substitute the given values into the equation:

Calculate the numerator:

Now, divide by the pressure ($1.58$):

Rounding to two decimal places, we get 14.84 dm$^3$.

4. Identify the Answer

Comparing our result to the given options, the correct value is 14.84 dm$^3$. This matches option A.

5. Exam Tip

Always check your units before calculating! In JAMB Chemistry, a very common trap is forgetting to convert Celsius to Kelvin. If you had used 13 directly in the formula, your answer would have been completely wrong. Always add 273 to your Celsius temperature first.