A fixed quantity of gas at 25 _x001F_C exhibits a pressure of 99 ...

Question

A fixed quantity of gas at 25 _x001F_C exhibits a pressure of 99 kPa and occupies a volume of 4.00 L. (a) Calculate the volume the gas will occupy if the pressure is increased to 202.6 kPa while the temperature is held constant. (b) Calculate the volume the gas will occupy if the temperature is increased to 100 °C while the pressure is held constant.

Accepted Answer

Step 1: Identify the initial conditions for both parts of the problem. For part (a), the initial pressure $ P_1 $ is 99 kPa, and the initial volume $ V_1 $ is 4.00 L. For part (b), the initial temperature $ T_1 $ is 25 °C, which needs to be converted to Kelvin.. Step 2: For part (a), use Boyle's Law, which states that $ P_1 V_1 = P_2 V_2 $ when temperature is constant. Rearrange the equation to solve for the final volume $ V_2 $: $ V_2 = \frac{P_1 V_1}{P_2} $. Substitute the known values: $ P_1 = 99 $ kPa, $ V_1 = 4.00 $ L, and $ P_2 = 202.6 $ kPa.. Step 3: For part (b), convert the initial temperature from Celsius to Kelvin by adding 273.15: $ T_1 = 25 + 273.15 $. The final temperature $ T_2 $ is 100 °C, which also needs to be converted to Kelvin: $ T_2 = 100 + 273.15 $.. Step 4: Use Charles's Law for part (b), which states that $ \frac{V_1}{T_1} = \frac{V_2}{T_2} $ when pressure is constant. Rearrange the equation to solve for the final volume $ V_2 $: $ V_2 = V_1 \times \frac{T_2}{T_1} $. Substitute the known values: $ V_1 = 4.00 $ L, $ T_1 $ and $ T_2 $ in Kelvin.. Step 5: Calculate the final volumes for both parts using the rearranged equations and substituted values.