Determine The Volume Of Gas Collected Over Water When 0.501 G O, Is Produced By The Lecomposition Of KCIO, At 35.0°C And 1.08 Atm.
Understanding the Problem
In this problem, we are tasked with determining the volume of gas collected over water when 0.501 g of oxygen (O2) is produced by the decomposition of potassium chlorate (KClO3) at a temperature of 35.0°C and a pressure of 1.08 atm. To solve this problem, we will need to use the ideal gas law, which relates the pressure, volume, and temperature of a gas.
The Ideal Gas Law
The ideal gas law is given by the equation:
PV = nRT
where P is the pressure of the gas, V is the volume of the gas, n is the number of moles of the gas, R is the gas constant, and T is the temperature of the gas in Kelvin.
Converting the Temperature to Kelvin
The temperature given in the problem is 35.0°C. To convert this temperature to Kelvin, we can use the following equation:
T (K) = T (°C) + 273.15
Plugging in the value of the temperature, we get:
T (K) = 35.0 + 273.15 = 308.15 K
Calculating the Number of Moles of Oxygen
To calculate the number of moles of oxygen produced, we can use the molar mass of oxygen, which is 32.00 g/mol. We can then use the following equation:
n = mass of oxygen / molar mass of oxygen
Plugging in the values, we get:
n = 0.501 g / 32.00 g/mol = 0.0156 mol
Using the Ideal Gas Law to Calculate the Volume
Now that we have the number of moles of oxygen, we can use the ideal gas law to calculate the volume of the gas. We can rearrange the equation to solve for V:
V = nRT / P
Plugging in the values, we get:
V = (0.0156 mol)(0.08206 L atm/mol K)(308.15 K) / (1.08 atm)
V = 0.373 L
Calculating the Volume of Gas Collected Over Water
However, the problem states that the gas is collected over water. This means that the volume of the gas we calculated is not the final answer. We need to subtract the volume of the water displaced by the gas from the total volume.
The Volume of Water Displaced
To calculate the volume of water displaced, we can use the density of water, which is 1.00 g/mL. We can then use the following equation:
volume of water displaced = mass of water displaced / density of water
Since the mass of water displaced is equal to the mass of oxygen produced, we can plug in the values:
volume of water displaced = 0.501 g / 1.00 g/mL = 0.501 mL
Converting the Volume of Water Displaced to Liters
To convert the volume of water displaced from milliliters to liters, we can use the following equation:
volume of water displaced (L) = volume of water displaced (mL) / 1000
Plugging in the value, we get:
volume of water displaced (L) = 0.501 mL / 1000 = 0.000501 L
Calculating the Final Volume of Gas Collected Over Water
Now that we have the volume of water displaced, we can subtract it from the total volume to get the final volume of gas collected over water:
final volume of gas collected over water = total volume - volume of water displaced
Plugging in the values, we get:
final volume of gas collected over water = 0.373 L - 0.000501 L = 0.3725 L
Conclusion
In this problem, we were tasked with determining the volume of gas collected over water when 0.501 g of oxygen is produced by the decomposition of potassium chlorate at a temperature of 35.0°C and a pressure of 1.08 atm. We used the ideal gas law to calculate the volume of the gas, and then subtracted the volume of water displaced to get the final volume of gas collected over water.
References
- Ideal Gas Law: The ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, and temperature of a gas.
- Molar Mass of Oxygen: The molar mass of oxygen is 32.00 g/mol.
- Density of Water: The density of water is 1.00 g/mL.
Additional Information
- Decomposition of Potassium Chlorate: The decomposition of potassium chlorate is a chemical reaction that produces oxygen gas.
- Ideal Gas Law Calculator: An ideal gas law calculator can be used to calculate the volume of a gas given the pressure, temperature, and number of moles.
Related Topics
- Chemical Reactions: Chemical reactions involve the transformation of one or more substances into new substances.
- Gas Laws: Gas laws are mathematical relationships that describe the behavior of gases.
- Chemical Equilibrium: Chemical equilibrium is a state in which the rates of forward and reverse reactions are equal.
Q&A: Determining the Volume of Gas Collected Over Water =====================================================
Frequently Asked Questions
In this article, we will answer some of the most frequently asked questions related to determining the volume of gas collected over water.
Q: What is the ideal gas law?
A: The ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, and temperature of a gas. It is given by the equation:
PV = nRT
where P is the pressure of the gas, V is the volume of the gas, n is the number of moles of the gas, R is the gas constant, and T is the temperature of the gas in Kelvin.
Q: How do I calculate the number of moles of oxygen produced?
A: To calculate the number of moles of oxygen produced, you can use the molar mass of oxygen, which is 32.00 g/mol. You can then use the following equation:
n = mass of oxygen / molar mass of oxygen
Q: What is the significance of the temperature in the ideal gas law?
A: The temperature in the ideal gas law is a measure of the average kinetic energy of the gas molecules. It is an important factor in determining the volume of the gas.
Q: How do I calculate the volume of water displaced by the gas?
A: To calculate the volume of water displaced by the gas, you can use the density of water, which is 1.00 g/mL. You can then use the following equation:
volume of water displaced = mass of water displaced / density of water
Q: What is the difference between the total volume and the final volume of gas collected over water?
A: The total volume is the volume of the gas calculated using the ideal gas law, while the final volume of gas collected over water is the total volume minus the volume of water displaced.
Q: Can I use the ideal gas law calculator to calculate the volume of the gas?
A: Yes, you can use the ideal gas law calculator to calculate the volume of the gas given the pressure, temperature, and number of moles.
Q: What are some related topics to the ideal gas law?
A: Some related topics to the ideal gas law include chemical reactions, gas laws, and chemical equilibrium.
Q: How do I determine the volume of gas collected over water when the pressure is not 1 atm?
A: To determine the volume of gas collected over water when the pressure is not 1 atm, you can use the ideal gas law and adjust the pressure accordingly.
Q: Can I use the ideal gas law to calculate the volume of a gas at a temperature other than 0°C?
A: Yes, you can use the ideal gas law to calculate the volume of a gas at a temperature other than 0°C. You will need to convert the temperature to Kelvin using the following equation:
T (K) = T (°C) + 273.15
Q: What is the significance of the gas constant in the ideal gas law?
A: The gas constant is a fundamental constant that relates the pressure, volume, and temperature of a gas. It is an important factor in determining the volume of the gas.
Q: Can I use the ideal gas law to calculate the volume of a gas at a pressure other than 1 atm?
A: Yes, you can use the ideal gas law to calculate the volume of a gas at a pressure other than 1 atm. You will need to adjust the pressure accordingly.
Q: How do I determine the volume of gas collected over water when the number of moles of gas is not known?
A: To determine the volume of gas collected over water when the number of moles of gas is not known, you can use the ideal gas law and the molar mass of the gas to calculate the number of moles.
Q: What are some common mistakes to avoid when using the ideal gas law?
A: Some common mistakes to avoid when using the ideal gas law include:
- Not converting the temperature to Kelvin
- Not using the correct units for the pressure and volume
- Not using the correct value for the gas constant
- Not adjusting the pressure accordingly
Conclusion
In this article, we have answered some of the most frequently asked questions related to determining the volume of gas collected over water. We hope that this article has been helpful in clarifying any doubts you may have had about the ideal gas law and its applications.