1. A 53.45 L automobile airbag, has a pressure of 705 mmHg. Under constant temperature, the airbag’s pressure was changed to 517 mmHg. What would be the final volume of a gas?
Make a conclusion about the relationship of pressure and volume.
2. Suppose you have a sample of CO2 in a gas-tight syringe. The gas volume is 30.5 mL at a temperature of 20.5 °C. What is the final volume of the gas if you hold the syringe in your hand to raise the temperature to 37.5 °C? Express your answer in L.
Make a conclusion about the relationship of temperature and volume.
3. A sealed container is filled with a gas to a pressure of 2.15 atm at 150°C. At what temperature would the pressure be 1.15 atm?
Make a conclusion about the relationship of pressure and temperature.
Make a conclusion about the relationship of pressure and volume.
2. Suppose you have a sample of CO2 in a gas-tight syringe. The gas volume is 30.5 mL at a temperature of 20.5 °C. What is the final volume of the gas if you hold the syringe in your hand to raise the temperature to 37.5 °C? Express your answer in L.
Make a conclusion about the relationship of temperature and volume.
3. A sealed container is filled with a gas to a pressure of 2.15 atm at 150°C. At what temperature would the pressure be 1.15 atm?
Make a conclusion about the relationship of pressure and temperature.
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Answer:
1. Using the combined gas law equation (P1V1/T1 = P2V2/T2), we can find the final volume of the gas:
V2 = (P1V1T2) / (T1P2) = (705 mmHg x 53.45 L x 273 K) / (298 K x 517 mmHg) = 64.28 L
Therefore, the final volume of the gas would be 64.28 L.
Conclusion: The relationship between pressure and volume is inverse (i.e., when pressure increases, volume decreases and vice versa) as long as temperature and the amount of gas remain constant, according to Boyle's law.
2. To find the final volume of the gas, we can use the ideal gas law equation (PV = nRT) and solve for the final volume (V2) using the initial volume (V1) and temperature (T1) as well as the new temperature (T2):
V2 = (nRT2) / P = (nRT1 x T2) / (P x T1) = (V1 x T2) / T1
V2 = (30.5 mL x 310.5 K) / 293.5 K = 32.2 mL = 0.0322 L
Therefore, the final volume of the gas would be 0.0322 L.
Conclusion: The relationship between temperature and volume is directly proportional (i.e., when temperature increases, volume also increases and vice versa) as long as pressure and the amount of gas remain constant, according to Charles's law.
3. We can use the combined gas law equation (P1V1/T1 = P2V2/T2) to find the final temperature (T2) using the initial pressure (P1), initial temperature (T1), and final pressure (P2):
T2 = (P2V1T1) / (P1V2) = (1.15 atm x V1 x 423 K) / (2.15 atm x V2)
We don't have enough information about the volume of gas or the initial pressure, so we cannot solve for the final temperature.
Conclusion: The relationship between pressure and temperature is also directly proportional (i.e., when temperature increases, pressure also increases and vice versa) as long as volume and the amount of gas remain constant, according to Gay-Lussac's law.
1. To solve for the final volume of the gas, we can use the formula:
P1V1 = P2V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Plugging in the given values, we get:
705 mmHg x 53.45 L = 517 mmHg x V2
Solving for V2, we get:
V2 = (705 mmHg x 53.45 L) / 517 mmHg
V2 = 72.85 L
Therefore, the final volume of the gas is 72.85 L.
Conclusion: This problem illustrates Boyle's Law, which states that at constant temperature, the pressure and volume of a gas are inversely proportional. As the pressure of the gas decreases, the volume increases proportionally.
2. To solve for the final volume of the gas, we can use the formula:
V2 = (V1/T1) x T2
where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
First, we need to convert the initial volume to liters and the temperature to Kelvin:
V1 = 30.5 mL = 0.0305 L
T1 = 20.5 °C + 273.15 = 293.65 K
T2 = 37.5 °C + 273.15 = 310.65 K
Plugging in the values, we get:
V2 = (0.0305 L/293.65 K) x 310.65 K
V2 = 0.0319 L
Therefore, the final volume of the gas is 0.0319 L.
Conclusion: This problem illustrates Charles's Law, which states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature. As the temperature of the gas increases, the volume increases proportionally.
3. To solve for the final temperature of the gas, we can use the formula:
P1/T1 = P2/T2
where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.
Plugging in the given values, we get:
2.15 atm / 423.15 K = 1.15 atm / T2
Solving for T2, we get:
T2 = (1.15 atm x 423.15 K) / 2.15 atm
T2 = 227.15 K
Therefore, the final temperature of the gas is 227.15 K.
Conclusion: This problem illustrates Gay-Lussac's Law, which states that at constant volume, the pressure and temperature of a gas are directly proportional. As the pressure of the gas decreases, the temperature decreases proportionally.