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#chemistry
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#gas-laws
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A sample of gas occupies 400ml at STP.under what pressure would this sample occupy 200ml,if the temperature were increased to 819°c?

Dec 16, 2023

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Dec 16, 2023

To solve this problem, we can use the combined gas law equation:

(P1 * V1) / (T1) = (P2 * V2) / (T2)

Where:

P1 = initial pressure (STP = 1 atm)

V1 = initial volume (400 ml)

T1 = initial temperature (STP = 273 K)

P2 = final pressure (unknown)

V2 = final volume (200 ml)

T2 = final temperature (819 °C = 1092 K)

Plugging in the values:

(1 atm * 400 ml) / (273 K) = (P2 * 200 ml) / (1092 K)

Simplifying the equation:

400 / 273 = (P2 * 200) / 1092

Cross-multiplying:

P2 * 200 = (400 / 273) * 1092

P2 * 200 = 1.584 * 1092

P2 * 200 = 1728.768

Dividing both sides by 200:

P2 = 1728.768 / 200

P2 = 8.64384

Therefore, the pressure at which the sample would occupy 200 ml at a temperature of 819 °C is approximately 8.64 atm.

(P1 * V1) / (T1) = (P2 * V2) / (T2)

Where:

P1 = initial pressure (STP = 1 atm)

V1 = initial volume (400 ml)

T1 = initial temperature (STP = 273 K)

P2 = final pressure (unknown)

V2 = final volume (200 ml)

T2 = final temperature (819 °C = 1092 K)

Plugging in the values:

(1 atm * 400 ml) / (273 K) = (P2 * 200 ml) / (1092 K)

Simplifying the equation:

400 / 273 = (P2 * 200) / 1092

Cross-multiplying:

P2 * 200 = (400 / 273) * 1092

P2 * 200 = 1.584 * 1092

P2 * 200 = 1728.768

Dividing both sides by 200:

P2 = 1728.768 / 200

P2 = 8.64384

Therefore, the pressure at which the sample would occupy 200 ml at a temperature of 819 °C is approximately 8.64 atm.