Question

Find the temperature in degree Celsius if the volume and pressure of 2 moles of an ideal gas are $20\,\text{dm}^3$ and $4.926\,\text{atm}$ respectively. ($R = 0.0821\,\text{dm}^3\text{atm K}^{-1}\text{mol}^{-1}$)

• A. 273
• B. 327
• C. 600
• D. 453

Hint:

Chemistry Tip: Always double-check the requested units for the final answer. The ideal gas law inherently outputs temperature in Kelvin. Failing to convert it back to Celsius (Option C vs Option B) is a very common trap.

Answer 1

The Correct Option is B

Concept: Chemistry (States of Matter) - Ideal Gas Law.

Step 1: Identify the given parameters and their units. Number of moles ($n$) = 2 mol. Volume ($V$) = $20~dm^{3}$ (which is equivalent to 20 Liters). Pressure ($P$) = $4.926\text{ atm}$. Universal Gas Constant ($R$) = $0.0821~dm^{3}\text{atm } K^{-1}mol^{-1}$.

Step 2: State the Ideal Gas Equation. The behavior of an ideal gas is described by the equation $PV = nRT$, where $T$ is the absolute temperature measured in Kelvin ($K$).

Step 3: Rearrange the formula to solve for Temperature ($T$). To find the temperature, isolate $T$ on one side of the equation: $T = \frac{PV}{nR}$.

Step 4: Substitute the values and calculate the temperature in Kelvin. Plug the given values into the rearranged equation: $T = \frac{(4.926\text{ atm}) \times (20~dm^{3})}{(2\text{ mol}) \times (0.0821~dm^{3}\text{atm } K^{-1}mol^{-1})}$. First, calculate the numerator: $4.926 \times 20 = 98.52$. Next, calculate the denominator: $2 \times 0.0821 = 0.1642$. Now, divide the numerator by the denominator: $T = \frac{98.52}{0.1642} = 600\text{ K}$.

Step 5: Convert the temperature from Kelvin to degrees Celsius. The question specifically asks for the temperature in degrees Celsius ($^{\circ}C$). The relationship between Kelvin and Celsius is $T(^{\circ}C) = T(K) - 273.15$ (often approximated as 273 for simpler calculations). $T(^{\circ}C) = 600 - 273 = 327^{\circ}C$. $$ \therefore \text{The temperature of the gas is } 327^{\circ}C. $$