You are given a gas at 750 torr with a volume of 0.62 L at 25°C. A while later, you measure the temperature and notice a 5°C temperature increase in the system. Assuming there is no pressure change and that this is an ideal gas, what is the new volume?

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Asked on June 25, 2026Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

Accepted Answer · 2026-06-25T09:28:11.601Z

Here are the solutions for questions 2 and 3. Question 2: Step 1: Convert initial and final temperatures to Kelvin. The initial temperature T_1 = 25^. T_1 = 25 + 273.15 = 298.15 \, K The temperature increases by 5^, so the final temperature T_2 = 25^ + 5^ = 30^. T_2 = 30 + 273.15 = 303.15 \, K Step 2: Apply Charles's Law. Since the pressure is constant, we can use Charles's Law, which states that for a fixed amount of gas at constant pressure, the volume is directly proportional to its absolute temperature: (V_1)/(T_1) = (V_2)/(T_2) We are given V_1 = 0.62 \, L. We need to find V_2. Rearrange the formula to solve for V_2: V_2 = V_1 × (T_2)/(T_1) Step 3: Substitute the values and calculate the new volume. V_2 = 0.62 \, L × 303.15 \, K298.15 \, K V_2 = 0.62 \, L × 1.01676 V_2 ≈ 0.63039 \, L Rounding to two significant figures, the new volume is 0.63 \, L. The final answer is 0.63 L. Question 3: Step 1: Convert temperature to Kelvin and pressure to atmospheres. The given temperature T = 30^. T = 30 + 273.15 = 303.15 \, K The given pressure P = 780 \, torr. Convert torr to atmospheres (1 atm = 760 torr): P = 780 \, torr × 1 \, atm760 \, torr ≈ 1.0263 \, atm The given density = 3.33 \, g/L. The ideal gas constant R = 0.08206 \, L · atm / (mol · K). Step 2: Use the ideal gas law in terms of density and molar mass. The ideal gas law is PV = nRT. We know that the number of moles n = (m)/(M), where m is mass and M is molar mass. Substituting n into the ideal gas law: PV = (m)/(M)RT Rearranging to solve for molar mass M: M = (mRT)/(PV) Since density = (m)/(V), we can substitute (m)/(V) with : M = ( RT)/(P) Step 3: Substitute the values and calculate the molar mass. M = (3.33 \, g/L)(0.08206 \, L · atm / (mol · K))(303.15 \, K)1.0263 \, atm M = (82.906)/(1.0263) \, g/mol M ≈ 80.78 \, g/mol Rounding to three significant figures, the molar mass is 80.8 \, g/mol. The final answer is 80.8 g/mol. 3 done, 2 left today. You're making progress.

Accepted Answer · 2026-06-25T09:28:11.601Z

Here are the solutions for questions 2 and 3. Question 2: Step 1: Convert initial and final temperatures to Kelvin. The initial temperature T_1 = 25^. T_1 = 25 + 273.15 = 298.15 \, K The temperature increases by 5^, so the final temperature T_2 = 25^ + 5^ = 30^. T_2 = 30 + 273.15 = 303.15 \, K Step 2: Apply Charles's Law. Since the pressure is constant, we can use Charles's Law, which states that for a fixed amount of gas at constant pressure, the volume is directly proportional to its absolute temperature: (V_1)/(T_1) = (V_2)/(T_2) We are given V_1 = 0.62 \, L. We need to find V_2. Rearrange the formula to solve for V_2: V_2 = V_1 × (T_2)/(T_1) Step 3: Substitute the values and calculate the new volume. V_2 = 0.62 \, L × 303.15 \, K298.15 \, K V_2 = 0.62 \, L × 1.01676 V_2 ≈ 0.63039 \, L Rounding to two significant figures, the new volume is 0.63 \, L. The final answer is 0.63 L. Question 3: Step 1: Convert temperature to Kelvin and pressure to atmospheres. The given temperature T = 30^. T = 30 + 273.15 = 303.15 \, K The given pressure P = 780 \, torr. Convert torr to atmospheres (1 atm = 760 torr): P = 780 \, torr × 1 \, atm760 \, torr ≈ 1.0263 \, atm The given density = 3.33 \, g/L. The ideal gas constant R = 0.08206 \, L · atm / (mol · K). Step 2: Use the ideal gas law in terms of density and molar mass. The ideal gas law is PV = nRT. We know that the number of moles n = (m)/(M), where m is mass and M is molar mass. Substituting n into the ideal gas law: PV = (m)/(M)RT Rearranging to solve for molar mass M: M = (mRT)/(PV) Since density = (m)/(V), we can substitute (m)/(V) with : M = ( RT)/(P) Step 3: Substitute the values and calculate the molar mass. M = (3.33 \, g/L)(0.08206 \, L · atm / (mol · K))(303.15 \, K)1.0263 \, atm M = (82.906)/(1.0263) \, g/mol M ≈ 80.78 \, g/mol Rounding to three significant figures, the molar mass is 80.8 \, g/mol. The final answer is 80.8 g/mol. 3 done, 2 left today. You're making progress.

You are given a gas at 750 torr with a volume of 0.62 L at 25°C. A while later, you measure the temperature and notice a 5°C temperature increase in the system. Assuming there is no pressure change and that this is an ideal gas, what is the new volume?

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You are given a gas at 750 torr with a volume of 0.62 L at 25°C. A while later, you measure the temperature and notice a 5°C temperature increase in the system. Assuming there is no pressure change and that this is an ideal gas, what is the new volume?

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