A gas occuies 100.0ml at 50degree c and 1 atm pressure. The gas is cooled at constan pressure so that volume is reduced to 50ml. What is final temperature of the gas?

To find the final temperature of the gas after it has been cooled at constant pressure, we can use Charles's Law. This law states that the volume of a gas is directly proportional to its temperature (in Kelvin) when the pressure is held constant. The formula for Charles's Law is:

Charles's Law Formula

The formula can be expressed as:

V1 / T1 = V2 / T2

Where:

• V1 = initial volume of the gas
• T1 = initial temperature of the gas (in Kelvin)
• V2 = final volume of the gas
• T2 = final temperature of the gas (in Kelvin)

Step-by-Step Calculation

Let's break down the problem step by step:

1. Convert Initial Temperature to Kelvin

The initial temperature is given as 50 degrees Celsius. To convert this to Kelvin, you add 273.15:

T1 = 50 + 273.15 = 323.15 K

2. Identify the Initial and Final Volumes

From the problem, we know:

• V1 = 100.0 mL
• V2 = 50.0 mL

3. Rearranging Charles's Law

We need to find T2, so we rearrange the formula:

T2 = (V2 * T1) / V1

4. Plugging in the Values

Now we can substitute the known values into the rearranged formula:

T2 = (50.0 mL * 323.15 K) / 100.0 mL

5. Performing the Calculation

Calculating this gives:

T2 = (16157.5 K*mL) / 100.0 mL = 161.575 K

Final Temperature in Celsius

To convert the final temperature back to Celsius, we subtract 273.15:

T2 (Celsius) = 161.575 K - 273.15 = -111.575 °C

Summary

The final temperature of the gas, after being cooled at constant pressure and reducing its volume from 100.0 mL to 50.0 mL, is approximately -111.58 °C. This example illustrates how gases behave under changing conditions, and Charles's Law provides a clear method for calculating the relationships between volume and temperature.