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Chapter 5: Problem 57

A 2.50-L container is filled with 175 g argon. a. If the pressure is 10.0 atm, what is the temperature? b. If the temperature is 225 K, what is the pressure?

Short Answer

Expert verified
a. The temperature when the pressure is 10.0 atm is approximately 694 K. b. The pressure when the temperature is 225 K is approximately 16.14 atm.

Step by step solution

01

Convert mass of argon to moles

To convert the mass of argon (m = 175 g) to moles (n), we'll use the molar mass of argon (Ar = 39.95 g/mol): n = m / Ar n = 175 g / 39.95 g/mol
02

Calculate the moles of argon

Using the formula from Step 1, we get: n = 175 g / 39.95 g/mol n ≈ 4.38 moles
03

Part a: Find the temperature when the pressure is 10.0 atm

Using the ideal gas law equation (PV = nRT), we can solve for the temperature (T). We know: P = 10.0 atm V = 2.50 L n = 4.38 moles R = 0.08206 L·atm/mol·K (ideal gas constant) Rearrange the ideal gas law equation to solve for T: T = PV / (nR) Now, plug in the given values: T = (10.0 atm) × (2.50 L) / (4.38 moles × 0.08206 L·atm/mol·K)
04

Calculate the temperature when the pressure is 10.0 atm

Using the formula from Step 3, we get: T = (10.0 atm) × (2.50 L) / (4.38 moles × 0.08206 L·atm/mol·K) T ≈ 694 K So, the temperature when the pressure is 10.0 atm is approximately 694 K.
05

Part b: Find the pressure when the temperature is 225 K

Using the ideal gas law equation (PV = nRT), we can solve for the pressure (P). We know: V = 2.50 L n = 4.38 moles R = 0.08206 L·atm/mol·K (ideal gas constant) T = 225 K Rearrange the ideal gas law equation to solve for P: P = nRT / V Now, plug in the given values: P = (4.38 moles × 0.08206 L·atm/mol·K × 225 K) / (2.50 L)
06

Calculate the pressure when the temperature is 225 K

Using the formula from Step 5, we get: P = (4.38 moles × 0.08206 L·atm/mol·K × 225 K) / (2.50 L) P ≈ 16.14 atm So, the pressure when the temperature is 225 K is approximately 16.14 atm.

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