Question

A sealed container holding 0.0250L of carbon dioxide gas at 0.977atm and 75.0°C is placed in a refrigerator and cooled to 19°C and the pressure drops to 0.851atm. What's the new volume?

Answer 1

To find the new volume, you can use the ideal gas law equation PV = nRT. Convert the temperatures from Celsius to Kelvin and plug in the given values into the equation V1 / P1 = V2 / P2. Solve for V2 to get the new volume.

Step-by-step explanation:

To solve this problem, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin. Since we are asked to find the new volume, we can rearrange the equation to solve for V: V = (nRT) / P.

First, we need to convert the given temperatures from Celsius to Kelvin. To convert from Celsius to Kelvin, we add 273.15. So the initial temperature of 75.0°C is 75.0 + 273.15 = 348.15K, and the final temperature of 19°C is 19 + 273.15 = 292.15K.

Now we can plug in the given values into the equation: V1 = (n1 * R * T1) / P1, and V2 = (n2 * R * T2) / P2. Since the number of moles and the ideal gas constant are constant, they cancel out. Therefore, we get the equation: V1 / P1 = V2 / P2.

Substituting the given values: 0.0250L / 0.977atm = V2 / 0.851atm. Solving for V2, we get V2 = 0.0250L * 0.851atm / 0.977atm = 0.0217L.