What must the Celsius temperature be if \(2.0\) moles of a gas in a 4.0-L steel container has a measured pressure of \(100 \mathrm{~atm} ?\)

Short Answer

Expert verified
The Celsius temperature of the gas in the container is approximately 2162.41 °C.

Step by step solution

01

List the given values

We have the following given values: - moles of gas (n) = 2.0 moles - volume of the gas (V) = 4.0 L - pressure of the gas (P) = 100 atm - ideal gas constant (R) = 0.0821 L atm/mol K
02

Apply Ideal Gas Law formula

Now we should use the Ideal Gas Law formula to find the temperature in Kelvin (T): PV = nRT, 100 * 4.0 = 2.0 * 0.0821 * T, Solving for T: T = (100 * 4.0) / (2.0 * 0.0821)
03

Calculate the temperature in Kelvin

Compute the value of T by substituting the given values in the above equation: T = (400) / (0.1642) ≈ 2435.56 K
04

Convert the temperature from Kelvin to Celsius

To find the Celsius temperature, convert the temperature from Kelvin to Celsius using the formula: T(°C) = T(K) - 273.15, T(°C) = 2435.56 - 273.15 ≈ 2162.41 °C Thus, the Celsius temperature of the gas in the container is about 2162.41 °C.

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