To calculate the temperature of the ideal gas sample, we use the Ideal Gas Law:

$PV = nRT$

Given values:

• $P = 2.00 \, \text{atm}$ (pressure)
• $V = 0.00200 \, \text{m}^3$ (volume)
• $n = 0.250 \, \text{moles}$ (amount of gas)
• $R = 8.314 \, \text{J/(mol·K)}$ (universal gas constant, note we need pressure in pascals)

Step 1: Convert pressure to pascals

1 atmosphere (atm) = $101325 \, \text{Pa}$, so: $P = 2.00 \, \text{atm} \times 101325 \, \text{Pa/atm} = 202650 \, \text{Pa}$

Step 2: Solve for temperature $T$

Rearranging the Ideal Gas Law to solve for $T$: $T = \frac{PV}{nR}$

Substitute the values: $T = \frac{(202650 \, \text{Pa})(0.00200 \, \text{m}^3)}{(0.250 \, \text{mol})(8.314 \, \text{J/(mol·K)})}$

Step 3: Calculate

$T = \frac{405.3 \, \text{J}}{2.0785 \, \text{J/K}}$ $T \approx 195 \, \text{K}$

Final Answer:

The temperature of the gas sample is approximately 195 K.

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Do you want further clarification or detailed steps?
Here are 5 related questions to expand your understanding:

1. How does the Ideal Gas Law apply to real-world scenarios?
2. Why is it important to use Kelvin for temperature in gas law calculations?
3. What happens if the pressure or volume changes for this gas sample?
4. How would the calculation change if the gas was not ideal?
5. What are common units used for the gas constant $R$, and how do we convert them?

Tip: Always ensure units are consistent when using the Ideal Gas Law, especially for $R$.