Ozone is depleted in the stratosphere by chlorine from CF3Cl according to the following set of equations:
CF3Cl+UV light-->CF3+Cl
Cl+O3-->ClO+O2
O3+UV light-->O2+O
ClO+O-->Cl+O2
What total volume of ozone measured at a pressure of 22.0 mmHg and a temperature of 220 K can be destroyed when all of the chlorine from 20.0 g of CF3Cl goes through ten cycles of the above reactions?
To calculate the total volume of ozone destroyed when all of the chlorine from CF3Cl goes through ten cycles of the reactions, we need to follow these steps:
1. Determine the moles of CF3Cl:
- Use the molar mass of CF3Cl to convert grams to moles.
- Molar mass of CF3Cl: C = 12.01 g/mol, F = 18.998 g/mol (3 fluorine atoms), Cl = 35.45 g/mol
- Calculate: (20.0 g CF3Cl) / (12.01 g/mol + 3 * 18.998 g/mol + 35.45 g/mol)
2. Calculate the moles of chlorine (Cl) present:
- Since each molecule of CF3Cl produces one chlorine atom, the moles of chlorine will be the same as the moles of CF3Cl.
3. Calculate the moles of O3 (ozone) destroyed in one cycle:
- From the balanced equation, we see that one mole of Cl reacts with one mole of O3 to produce one mole of ClO.
- So the moles of O3 destroyed in each cycle will be the same as the moles of Cl.
4. Calculate the total moles of O3 destroyed in ten cycles:
- Multiply the moles of O3 destroyed in one cycle by ten.
5. Convert the moles of O3 destroyed to volume:
- Use the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (0.08206 L·atm/(mol·K)), and T is the temperature in Kelvin.
- Rearrange the formula to solve for V: V = (nRT) / P
- Plug in the values of n, R, T, and P to calculate the volume.
Let's plug in the values and calculate step by step:
1. Moles of CF3Cl:
Molar mass of CF3Cl = 12.01 g/mol + 3 * 18.998 g/mol + 35.45 g/mol = 137.36 g/mol
Moles of CF3Cl = 20.0 g / 137.36 g/mol = ...
To continue the calculation, we need the value of the molar mass of CF3Cl that you didn't provide.
To find the total volume of ozone that can be destroyed, we need to calculate the amount of chlorine that reacts with ozone in each cycle and then determine the total volume of ozone destroyed by multiplying it by the number of cycles.
Given:
Pressure (P) = 22.0 mmHg
Temperature (T) = 220 K
Mass of CF3Cl (m) = 20.0 g
First, we need to convert the pressure from mmHg to atm by dividing it by 760 mmHg/atm:
P = 22.0 mmHg / 760 mmHg/atm = 0.02895 atm
Next, let's calculate the number of moles of CF3Cl:
Molar mass of CF3Cl = (1 x 12.01 g/mol) + (3 x 19.00 g/mol) + (1 x 35.45 g/mol) = 137.45 g/mol
Number of moles of CF3Cl = mass / molar mass = 20.0 g / 137.45 g/mol = 0.1456 mol
According to the balanced equation, 1 mol of CF3Cl produces 1 mol of Cl. Therefore, the number of moles of Cl is also 0.1456 mol.
In each cycle, 1 mol of Cl reacts with 1 mol of ozone (O3). So, in 10 cycles, we have:
10 cycles * 0.1456 mol = 1.456 mol
Now, we can use the ideal gas law to find the volume of ozone destroyed:
PV = nRT
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature = 220 K
V = (nRT) / P
V = (1.456 mol * 0.0821 L·atm/(mol·K) * 220 K) / 0.02895 atm
V ≈ 19.678 L
Therefore, the total volume of ozone destroyed after 10 cycles is approximately 19.678 liters.
Make sure the equations are balanced.
Follow the steps in this example for one set. Then multiply by 10 cycles.
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