Question

A gas sample has a volume of 150.0 mL at 30.00⁰C and 300.0 kPa. What will the pressure be if it is cooled to 20.00⁰C at a constant volume? Report your answer with four significant figures

Answer 1

The pressure of the gas sample will be 291.78 kPa when it is cooled to 20.00°C at a constant volume.

Step-by-step explanation:

When a gas sample is cooled at constant volume, the pressure of the gas decreases. The relationship between pressure and temperature for an ideal gas at constant volume is given by the equation:

P1/T1 = P2/T2

Where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature. It is important to note that the temperature must be in Kelvin in order to use this equation.

Using the given information, the initial pressure (P1) is 300.0 kPa, the initial temperature (T1) is 30.00°C + 273.15 = 303.15 K, and the final temperature (T2) is 20.00°C + 273.15 = 293.15 K. By rearranging the equation and solving for P2, we can find the final pressure:

P2 = (P1 * T2) / T1 = (300.0 kPa * 293.15 K) / 303.15 K = 291.78 kPa

Answer 2

The question relates to Gay-Lussac's Law. Using this law and the given information, we can calculate that the new pressure of the gas when it is cooled to 20.00⁰C at a constant volume will be approximately 290.2 kPa.

Step-by-step explanation:

The question basically deals with the concept of Gay-Lussac's Law, which is a principle in gas physics stating that the pressure of a gas is directly proportional to its absolute temperature, provided the volume remains constant. To solve this, we can use the formula: P1/T1 = P2/T2, where P denotes pressure and T is temperature (in Kelvin). Therefore, to find the new pressure, we can rearrange the formula: P2 = P1 * (T2/T1).

In this problem, convert the temperatures to Kelvin by adding 273.15 to each Celsius reading.

So, T1 is (30.00 + 273.15) = 303.15K and T2 is (20.00 + 273.15) = 293.15K.

The initial pressure P1 = 300.0 kPa. Substituting these values gives: P2 = 300.0 kPa * (293.15K/303.15K) = 290.2140 kPa. Therefore, when the gas is cooled to 20.00⁰C at a constant volume, the pressure is approximately 290.2 kPa.

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