Question

0.10 mol of argon gas is admitted to an evacuated 50 cm3 container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C. What is the final pressure of the gas?

Accepted Answer

Step 1: Start by identifying the given values and converting them into appropriate SI units. The initial number of moles of argon gas is $$ n = 0.10 \; 	ext{mol} . $$The volume of the container is $$ V = 50 \; 	ext{cm}^3 = 50 	imes 10^{-6} \; 	ext{m}^3 . $$The initial temperature is $$ T_1 = 20^\circ 	ext{C} = 20 + 273.15 = 293.15 \; 	ext{K} $$, and the final temperature is $$ T_2 = 300^\circ 	ext{C} = 300 + 273.15 = 573.15 \; 	ext{K} . $$Step 2: Use the ideal gas law to find the initial pressure of the gas. The ideal gas law is $$ PV = nRT $$, where $$ P  is $$the pressure, $$ V  is $$the volume, $$ n  is $$the number of moles, $$ R  is $$the universal gas constant $$ R = 8.314 \; 	ext{J/(mol·K)} $$, and $$ T  is $$the temperature. Rearrange the equation to solve for $$ P_1 $$: $$ P_1 = \frac{nRT_1}{V} . $$Substitute the known values to calculate $$ P_1 . $$Step 3: Recognize that the process is isochoric, meaning the volume remains constant. For an isochoric process, the pressure and temperature are related by the equation $$ \frac{P_1}{T_1} = \frac{P_2}{T_2} . $$Rearrange this equation to solve for the final pressure $$ P_2 $$: $$ P_2 = P_1 \cdot \frac{T_2}{T_1} . $$Step 4: Substitute the value of $$ P_1 $$ from Step 2 and the temperatures $$ T_1 $$ and $$ T_2 $$ into the equation from Step 3 to calculate $$ P_2 . $$Ensure that all units are consistent (e.g., temperature in Kelvin). Step 5: The final pressure $$ P_2  is $$the result of the calculation in Step 4. Express the answer in Pascals (Pa) or another appropriate unit of pressure, depending on the context of the problem.

0.10 mol of argon gas is admitted to an evacuated 50 cm³ container at 20°C. The gas then undergoes an isochoric heating to a temperature of 300°C. What is the final pressure of the gas?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Ideal Gas Law

Isochoric Process

Temperature Conversion