In an experiment, 25.0 ml of a gas with a pressure of 1. atm is contained in a balloon at 25.0 c. The Balloon is then cooled to 5.0 c, and the pressure is found to be .750 atm. What is the volume of the gas under the new conditions?
To solve this problem, we can use the combined gas law formula, which relates the initial and final conditions of temperature, pressure, and volume of a gas:
(P1 x V1) / (T1) = (P2 x V2) / (T2)
where:
P1 and P2 are the initial and final pressures,
V1 and V2 are the initial and final volumes,
T1 and T2 are the initial and final temperatures.
Let's plug in the given values into the formula:
(P1 x V1) / (T1) = (P2 x V2) / (T2)
(1.0 atm x 25.0 ml) / (25.0 °C) = (0.750 atm x V2) / (5.0 °C)
Now we need to solve for V2, the final volume.
To do that, we can rearrange the formula:
(1.0 atm x 25.0 ml) / (25.0 °C) = (0.750 atm x V2) / (5.0 °C)
25.0 ml / 25.0 °C = V2 / (0.750 atm x 5.0 °C)
Simplifying further:
1 ml / 1.0 °C = V2 / (0.750 atm x 5.0 °C)
V2 = (1 ml / 1.0 °C) x (0.750 atm x 5.0 °C)
V2 = 3.75 ml x atm / °C
Therefore, the volume of the gas under the new conditions is 3.75 ml.
To find the volume of the gas under the new conditions, we can use the combined gas law. The combined gas law relates the pressure, volume, and temperature of a gas. It can be written as:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume (unknown in this case)
T2 = final temperature
Let's substitute the given values into the equation and solve for V2:
P1 = 1.0 atm
V1 = 25.0 mL (which can be converted to liters by dividing by 1000: 25.0 mL / 1000 = 0.025 L)
T1 = 25.0 °C (which can be converted to Kelvin by adding 273: 25.0 °C + 273 = 298 K)
P2 = 0.750 atm
T2 = 5.0 °C (which can be converted to Kelvin: 5.0 °C + 273 = 278 K)
Now, let's plug in the values:
(1.0 atm * 0.025 L) / 298 K = (0.750 atm * V2) / 278 K
Simplifying the equation:
0.025 atm L / 298 K = (0.750 atm * V2) / 278 K
To solve for V2, we can cross-multiply and divide:
0.025 atm L * 278 K = 298 K * (0.750 atm * V2)
6.95 atm L = 223.5 atm L * V2
Dividing both sides by 223.5 atm L:
V2 = 6.95 / 223.5 L
Calculating the value:
V2 = 0.031 L or 31.0 mL
Therefore, the volume of the gas under the new conditions is 31.0 mL.
Use P1V1/t1=P2V2/T2
with T in kelvin (K)