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400.0mL of gas is collected over water at 24.0 C and 767.4 mmHg. Find its volume at standard conditions when dry

User TheRueger
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1 Answer

3 votes

Answer:

0.422 L

Step-by-step explanation:

To find the volume of gas at standard conditions when dry, we need to apply the concept of Dalton's Law of Partial Pressures and the ideal gas law.

Step 1: Convert the given pressure to atm units.

Given pressure: 767.4 mmHg

1 atm = 760 mmHg (by definition)

Pressure in atm = 767.4 mmHg / 760 mmHg/atm = 1.011 atm (rounded to three decimal places)

Step 2: Convert the given volume to liters.

Given volume: 400.0 mL

1 L = 1000 mL (by definition)

Volume in liters = 400.0 mL / 1000 mL/L = 0.400 L (rounded to three decimal places)

Step 3: Apply Dalton's Law of Partial Pressures.

Dalton's Law of Partial Pressures states that the total pressure of a gas mixture is the sum of the partial pressures of each gas component. In this case, we have two gases: the gas of interest and water vapor.

The partial pressure of water vapor at 24.0 °C is 23.76 mmHg (at 100% relative humidity). We need to subtract this from the total pressure to get the partial pressure of the gas of interest.

Partial pressure of gas of interest = Total pressure - Partial pressure of water vapor

Partial pressure of gas of interest = 1.011 atm - 23.76 mmHg / 760 mmHg/atm = 0.979 atm (rounded to three decimal places)

Step 4: Apply the ideal gas law to find the volume at standard conditions.

The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

At standard conditions, the pressure is 1 atm, and the temperature is 0 °C or 273.15 K.

R = 0.0821 L atm / (mol K) (ideal gas constant)

Rounded to three decimal places, the equation becomes:

(0.979 atm)(0.400 L) / (1 atm) = (n)(0.0821 L atm / (mol K))(273.15 K)

Solving for n (number of moles):

n = [(0.979 atm)(0.400 L)] / [(0.0821 L atm / (mol K))(273.15 K)] = 0.0186 mol (rounded to four decimal places)

Step 5: Find the volume of the gas at standard conditions using the molar volume of gases.

At standard conditions (0 °C or 273.15 K, 1 atm), the molar volume of an ideal gas is 22.71 L/mol.

Volume at standard conditions = n (molar volume of gas)

Volume at standard conditions = 0.0186 mol × 22.71 L/mol = 0.422 L (rounded to three decimal places)

So, the volume of the gas at standard conditions when dry is 0.422 L.

User Jason Hartley
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