KClO3 decomposes in the presence of MnO2 to form oxygen gas, collected over H2O at 23.0 degrees C and a barometric pressure of 754.2 torr, as described in the experimental description. After the pressure of the oxygen gas is equalized with atmospheric pressure, the mass of water collected is 386.2g. If the test tube plus KCLO3 initially weighed 45.850g and had a final mass of 45.351g, answer the following questions.
1. Calculate the number of moles of oxygen generated.
2. Calculate the volume of the gas generated, from the mass and density of water displaced.
3. Calculate the pressure of dry oxygen using Dalton's law of partial pressures.
4. Calculate the value of R, the gas constant, in L atm/mole K, and in mL torr/mole K.
Please help me!
1. The weight loss from 45.850g to 45.351g is the mass of oxygen, O2, gas released. The molar mass of O2 is 16.00x2 = 32.00g. This information should enable you get the moles of O2.
2. The volume of O2 = volume of water displaced.
volume = mass/density.
The density of water is very close to 1.00 g/mL
3. P(dry O2) = 754.2torr - P(water vapor)
Look up the vapor pressure of H2O at 23 deg C for the above calculation.
4. The Ideal Gas Law is PV = nRT
Convert the pressure of dry O2 to atmospheres.
Convert the volume of O2 to liters.
Convert 23.0 deg C to deg K
n is the number of moles of O2 from a previous calculation.
Substitute the above values into PV = nRT and solve for R.
no this is not correct because you guys do not have a brain
1. To calculate the number of moles of oxygen generated, we need to use the ideal gas law equation PV = nRT, where P is the pressure in atm, V is the volume in liters, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the pressure from torr to atm. Given that 1 atm = 760 torr, the pressure is:
754.2 torr / 760 torr/atm = 0.992 atm
Next, we need to convert the temperature from Celsius to Kelvin. The conversion formula is K = °C + 273.15. So the temperature is:
23.0 °C + 273.15 = 296.15 K
Since the test tube was initially weighed and the mass of water collected was measured, we can calculate the mass of oxygen generated by subtracting the mass of the water from the difference in mass of the test tube before and after:
Mass of oxygen = (45.850g - 45.351g) - 386.2g = -0.501g
Since the molar mass of oxygen (O2) is 32.00 g/mol, we can calculate the number of moles of oxygen generated:
Number of moles of oxygen = Mass of oxygen / molar mass of oxygen
Number of moles of oxygen = -0.501g / 32.00 g/mol = -0.0157 mol
Note: The negative sign indicates that there was a loss in mass, which is expected as oxygen gas is being produced.
2. To calculate the volume of gas generated using the mass and density of water displaced, we need to use the formula:
Volume of gas = Mass of water displaced / Density of water
Given that the mass of water collected is 386.2g, and the density of water at 23.0 °C is approximately 0.997 g/mL, we can calculate the volume of gas:
Volume of gas = 386.2g / 0.997 g/mL = 387 mL
3. Dalton's law of partial pressures states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each gas. In this case, the pressure of dry oxygen can be calculated by subtracting the vapor pressure of water at 23.0 °C from the total pressure.
The vapor pressure of water at 23.0 °C is approximately 21 torr. Therefore, the pressure of dry oxygen is:
Pressure of dry oxygen = Total pressure - Vapor pressure of water = 754.2 torr - 21 torr = 733.2 torr
4. The gas constant, R, can be found by using the ideal gas law equation PV = nRT rearranged to solve for R as R = PV / (nT).
To calculate R in L atm/mol K:
R = (Pressure of dry oxygen) * (Volume of gas) / (Number of moles of oxygen * Temperature)
R = (733.2 torr * 387 mL) / (0.0157 mol * 296.15 K)
R ≈ 62.36 L atm/mol K
To calculate R in mL torr/mol K:
R = (Pressure of dry oxygen) * (Volume of gas) / (Number of moles of oxygen * Temperature)
R = (733.2 torr * 387 mL) / (0.0157 mol * 296.15 K) * (1000 mL/L) * (1 atm/760 torr)
R ≈ 82.95 mL torr/mol K
Therefore, the value of R is approximately 62.36 L atm/mol K and 82.95 mL torr/mol K.
To answer the questions, we'll go step-by-step through the problem.
1. First, let's calculate the number of moles of oxygen generated.
- We know the mass of water collected, which is 386.2g. The molar mass of water (H2O) is 18.015 g/mol.
- To find the moles of oxygen, we need to assume that all the water collected came from the decomposition of KClO3. The reaction is:
2KClO3 → 2KCl + 3O2
- From the balanced equation, we see that for every 2 moles of KClO3 decomposed, 3 moles of O2 are produced.
- Therefore, we can use the molar ratio to find the moles of O2: (386.2g H2O) x (1 mol H2O / 18.015 g H2O) x (3 mol O2 / 2 mol KClO3) = ? mol O2
2. Next, let's calculate the volume of the gas generated.
- The density of water displaced can be determined using its mass and volume.
- The volume of water displaced can be calculated using the density of water, which is 1g/mL or 1g/cm^3.
- So, the volume of water displaced is equal to the mass of water collected, which is 386.2g.
- Hence, the volume of the gas generated is also equal to 386.2 mL.
3. Now, let's calculate the pressure of dry oxygen using Dalton's law of partial pressures.
- Dalton's law states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.
- The pressure of the dry oxygen can be found by subtracting the vapor pressure of water (which depends on the temperature) from the total pressure.
- The total pressure is given as 754.2 torr, and the vapor pressure of water at 23.0 degrees C is 21.1 torr (you can find this value in a vapor pressure table).
- Therefore, the pressure of dry oxygen is equal to 754.2 torr - 21.1 torr = ? torr.
4. Finally, let's calculate the value of R, the gas constant, in different units.
- The gas constant R can be calculated using the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, and T is the temperature measured in Kelvin.
- Rearranging the formula, R = PV / (nT).
- We can use the given values to calculate R:
- In L atm/mole K: R = (?? atm) x (?? L) / (?? mol) x (?? K)
- In mL torr/mole K: R = (?? mL) x (?? torr) / (?? mol) x (?? K)
Now, you just need to fill in the missing values from the problem statement and solve each question using the appropriate formulas and calculations described above.