Question

A gas sample has an initial volume of 55.2 mL, an initial temperature of 35.0 °C, and an initial pressure of 735 mm Hg. The volume is decreased to 48.8 mL and the temperature is increased to 72.5 °C. What is the final pressure?

Answer 1

To determine the final pressure of a gas when volume decreases and temperature increases, the combined gas law P1V1/T1 = P2V2/T2 is used. After converting temperatures to Kelvin, the equation is rearranged to solve for the final pressure.

Step-by-step explanation:

Calculating Final Pressure of a Gas

To find the final pressure of the gas when its volume is decreased and its temperature is increased, we can use the combined gas law which is represented by the equation: P1V1/T1 = P2V2/T2, where P is pressure, V is volume, and T is temperature in Kelvin.

First, convert the temperatures from Celsius to Kelvin (K = °C + 273.15). So, the initial temperature is 308.15 K (35.0 °C + 273.15) and the final temperature is 345.65 K (72.5 °C + 273.15).

Using the combined gas law: (735 mm Hg * 55.2 mL) / 308.15 K = P2 * 48.8 mL / 345.65 K. Solve for P2 to find the final pressure of the gas.

Answer 2

The answer to your question is P2 = 932.6 mmHg

Step-by-step explanation:

Data

Volume 1 = V1 = 55.2 ml

Temperature 1 = T1 = 35°C

Pressure 1 = P1 = 735 mmHg

Volume 2 = V2 = 48.8 ml

Temperature 2 = T2 = 72.5°C

Pressure 2 = P2 = ?

Process

1.- Convert temperature to °K

Temperature 1 = 35 + 273 = 308 °K

Temperature 2 = 72.5 + 273 = 345.5°K

2.- Use the Combine gas law to solve this problem

P1V1/T1 = P2V2/T2

-Solve for P2

P2 = P1V1T2 / T1V2

-Substitution

P2 = (735 x 55.2 x 345.5) / (308 x 48.8)

-Simplification

P2 = 14017626 / 15030.4

-Result

P2 = 932.6 mmHg