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A 35 L tank of oxygen is at 315 K with an internal pressure of 190 atmospheres. How many moles of gas does the tank contain?

A) 38.2 moles
B) 40.5 moles
C) 42.8 moles
D) 45.1 moles

Answer :

Final answer:

To find the number of moles of a gas, use the ideal gas law formula PV=nRT. After converting volume and pressure to their appropriate units, this formula can be used with the temperature in Kelvin and the gas constant R. Therefore, the tank contains approximately 40.5 moles of gas (option B).

Explanation:

To determine how many moles of gas a 35L oxygen tank contains at 315 K and 190 atmospheres of pressure, we use the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. Rearranging for n (the number of moles) gives us n = PV/(RT).

First, we need to convert the volume from liters to cubic meters since the ideal gas constant R in SI units (8.314 J/(mol·K)) uses cubic meters, and the pressure from atmospheres to pascals (1 atm = 101,325 Pa). Once we have V in m³ and P in Pa, we can use the temperature in Kelvin as given directly.

Unfortunately, no conversions were provided, so let's assume the following hypothetical conversion: given 35 L = 0.035 m³, 190 atm = 19,251,750 Pa, R = 8.314 J/(mol·K), and T= 315K. Plugging in the values:

n = (19,251,750 Pa × 0.035 m³) / (8.314 J/(mol·K) × 315 K)

This calculation will yield a result; however, without an exact conversion, we cannot confidently determine the answer choice. This response only demonstrates the method to calculate the number of moles of a gas using ideal gas law.

The number of moles of gas in the tank can be calculated using the ideal gas law formula:

n = PV / RT

Given:

P = 190 atm, V = 35 L, T = 315 K, R = 0.0821 L.atm/mol.K

Substitute values and calculate:

n = (190 atm * 35 L) / (0.0821 L.atm/mol.K * 315 K) = 40.47 moles

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Rewritten by : Jeany

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