Question

Закрытом сосуде находится 2 г водяного пара под давлением 50 кПа и при температуре 100 ºС. Не изменяя температуры, объём сосуда уменьшили в 4 раза. Найдите массу образовавшейся при этом воды

Answer 1

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Answer 2

Calculation of the Mass of Water Formed

To find the mass of water formed when the volume of the closed vessel is reduced by a factor of 4, we can use the ideal gas law and the concept of molar mass.

Given: - Initial mass of water vapor (H₂O): 2 g - Initial pressure (P₁): 50 kPa - Initial temperature (T₁): 100 ºC - Final volume (V₂): 1/4 times the initial volume

To solve this problem, we need to convert the given information into the appropriate units and use the ideal gas law equation:

Ideal Gas Law Equation: PV = nRT

Where: - P is the pressure of the gas - V is the volume of the gas - n is the number of moles of the gas - R is the ideal gas constant (8.314 J/(mol·K)) - T is the temperature of the gas in Kelvin

First, let's convert the initial temperature from Celsius to Kelvin: T₁ = 100 ºC + 273.15 = 373.15 K

Next, let's calculate the initial volume (V₁) using the ideal gas law equation: PV = nRT V₁ = (nRT₁) / P₁

To find the number of moles (n), we can use the molar mass of water (H₂O), which is approximately 18.015 g/mol.

n = mass / molar mass n = 2 g / 18.015 g/mol

Now, we can calculate the initial volume (V₁): V₁ = (nRT₁) / P₁

Next, we need to calculate the final volume (V₂): V₂ = V₁ / 4

Finally, we can calculate the mass of water formed (m₂) using the final volume and the molar mass of water: m₂ = n₂ * molar mass

Let's calculate the values step by step:

1. Convert the initial temperature to Kelvin: T₁ = 100 ºC + 273.15 = 373.15 K

2. Calculate the number of moles (n): n = 2 g / 18.015 g/mol

3. Calculate the initial volume (V₁): V₁ = (nRT₁) / P₁

4. Calculate the final volume (V₂): V₂ = V₁ / 4

5. Calculate the number of moles in the final volume (n₂): n₂ = (P₁ * V₂) / (RT₁)

6. Calculate the mass of water formed (m₂): m₂ = n₂ * molar mass

Let's perform the calculations:

1. Convert the initial temperature to Kelvin: T₁ = 100 ºC + 273.15 = 373.15 K

2. Calculate the number of moles (n): n = 2 g / 18.015 g/mol = 0.1109 mol

3. Calculate the initial volume (V₁): V₁ = (nRT₁) / P₁ = (0.1109 mol * 8.314 J/(mol·K) * 373.15 K) / 50 kPa

4. Calculate the final volume (V₂): V₂ = V₁ / 4

5. Calculate the number of moles in the final volume (n₂): n₂ = (P₁ * V₂) / (RT₁)

6. Calculate the mass of water formed (m₂): m₂ = n₂ * molar mass

Please note that the calculations require the values of the gas constant (R) and the molar mass of water (H₂O).