Question

1. using charles’ gas law, solve the following problem: a gas occupies 1.5 liters at 25 degrees celsius and constant pressure. if the temperature is increased to 100 degrees celsius what will the new volume be? $v_1 / t_1 = v_2/t_2$ use kelvin 273.15 for temp.

Explanation:

Step1: Convert Celsius to Kelvin for initial temperature

To convert Celsius to Kelvin, we use the formula \( T(K) = T(^\circ C) + 273.15 \). For \( T_1 = 25^\circ C \), we have \( T_1=25 + 273.15 = 298.15\ K \)

Step2: Convert Celsius to Kelvin for final temperature

For \( T_2 = 100^\circ C \), using the same formula \( T(K)=T(^\circ C)+ 273.15 \), we get \( T_2 = 100+ 273.15=373.15\ K \)

Step3: Rearrange Charles' Law to solve for \( V_2 \)

Charles' Law is \( \frac{V_1}{T_1}=\frac{V_2}{T_2} \). Rearranging for \( V_2 \), we get \( V_2=\frac{V_1\times T_2}{T_1} \)

Step4: Substitute the known values

We know that \( V_1 = 1.5\ L \), \( T_1 = 298.15\ K \) and \( T_2=373.15\ K \). Substituting these values into the formula for \( V_2 \), we have \( V_2=\frac{1.5\times373.15}{298.15} \)

Step5: Calculate the value of \( V_2 \)

First, calculate the numerator: \( 1.5\times373.15 = 559.725 \). Then divide by the denominator: \( \frac{559.725}{298.15}\approx1.88\ L \)

Answer:

The new volume of the gas is approximately \( 1.88 \) liters.