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25°C, a sample of gas in a closed system has a pressure of 125 kPa. In the volume is held constant and the temperature is

increased to 127°C, what is the new pressure of the gas?

1 Answer

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Answer:

To determine the new pressure of the gas, we can use Charles's Law, which states that the volume of a given amount of gas held at constant pressure is directly proportional to its temperature.

Charles's Law equation:

(V₁ / T₁) = (V₂ / T₂)

Where:

V₁ = Initial volume

T₁ = Initial temperature

V₂ = Final volume (held constant)

T₂ = Final temperature

In this case, the initial volume and the final volume are held constant, so we can rewrite the equation as:

(T₁ / P₁) = (T₂ / P₂)

Where:

P₁ = Initial pressure

P₂ = Final pressure

Now let's substitute the given values:

T₁ = 25°C = 25 + 273.15 = 298.15 K

P₁ = 125 kPa

T₂ = 127°C = 127 + 273.15 = 400.15 K

Plugging these values into the equation:

(298.15 K / 125 kPa) = (400.15 K / P₂)

To solve for P₂, we can cross-multiply and then divide:

(298.15 K) * P₂ = (125 kPa) * (400.15 K)

P₂ = (125 kPa * 400.15 K) / 298.15 K

P₂ ≈ 167.03 kPa

Therefore, the new pressure of the gas is approximately 167.03 kPa when the temperature is increased to 127°C while keeping the volume constant.

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