1. Use the Van der Waals equation to calculate the pressure exerted by 1.00 mol of Cl2; in 22.41 L at 0.0 degrees C. The constants for Cl are a = 6.49 L2 atm/mol2 and b = 0.0526 L/mol.
2. How much potassium chlorate is needed to produce 20.0 mL of oxygen at 670 mm Hg and 20 degrees C.
3. A certain compound containing only carbon and hydrogen was found to have a vapor density of 2.550 g/L at 100 degrees C and 760 mm Hg. If the empirical formula of this compound is CH, what is the molecular formula of this compound?
1. To calculate the pressure exerted by 1.00 mol of Cl2 using the Van der Waals equation, we will use the formula:
(p + a(n/V)^2)(V - nb) = nRT
where:
- p is the pressure we are trying to find
- a and b are the Van der Waals constants for Cl2
- n is the number of moles of Cl2 (1.00 mol)
- V is the volume of Cl2 (22.41 L)
- R is the ideal gas constant (0.0821 L·atm/mol·K)
- T is the temperature in Kelvin (0.0 degrees C + 273.15 = 273.15 K)
First, let's calculate (n/V)^2:
(n/V)^2 = (1.00 mol / 22.41 L)^2
Next, we can substitute the given values into the equation:
(p + a(n/V)^2)(V - nb) = nRT
(p + a(1.00 mol / 22.41 L)^2)(22.41 L - (0.0526 L/mol)(1.00 mol)) = (1.00 mol)(0.0821 L·atm/mol·K)(273.15 K)
Simplifying this equation will give us the value of p, which is the pressure exerted by 1.00 mol of Cl2 in 22.41 L at 0.0 degrees C.
2. To determine how much potassium chlorate is needed to produce 20.0 mL of oxygen at 670 mm Hg and 20 degrees Celsius, we will follow these steps:
Step 1: Convert the given conditions
- Convert 20.0 mL to liters by dividing it by 1000:
20.0 mL ÷ 1000 = 0.0200 L
- Convert the pressure of 670 mm Hg to atm by dividing it by 760:
670 mm Hg ÷ 760 mm Hg/atm = 0.8816 atm
- Convert the temperature of 20 degrees Celsius to Kelvin by adding 273.15:
20 degrees Celsius + 273.15 = 293.15 K
Step 2: Apply the ideal gas law equation
The ideal gas law is given by the formula:
PV = nRT
where:
- P is the pressure in atm
- V is the volume in liters
- n is the number of moles
- R is the ideal gas constant (0.0821 L·atm/mol·K)
- T is the temperature in Kelvin
Rearranging the formula to solve for n, the number of moles, we get:
n = PV / RT
Substituting the given values, we have:
n = (0.8816 atm)(0.0200 L) / (0.0821 L·atm/mol·K)(293.15 K)
Calculating the right side of the equation will give us the number of moles of oxygen produced.
3. To determine the molecular formula of a compound with empirical formula CH, given its vapor density is 2.550 g/L at 100 degrees C and 760 mm Hg, we will follow these steps:
Step 1: Calculate the molar mass of the empirical formula
The empirical formula CH has a molar mass of 12.01 g/mol (C) + 1.008 g/mol (H) = 13.018 g/mol.
Step 2: Calculate the molar mass of the compound
The molar mass of the compound can be calculated using the formula:
molar mass = vapor density x molar mass of H2 (the reference gas)
Given the vapor density is 2.550 g/L, and the molar mass of H2 is 2.016 g/mol, we can substitute these values into the formula:
molar mass of compound = 2.550 g/L x 2.016 g/mol
This will give us the molar mass of the compound.
Step 3: Determine the molecular formula
To find the molecular formula, we need to compare the molar mass of the compound with the molar mass of the empirical formula. Divide the molar mass of the compound by the molar mass of the empirical formula:
Molar mass of the compound / Molar mass of the empirical formula
If the result is a whole number or a simple ratio, the molecular formula is the same as the empirical formula. If it is not a whole number, multiply the empirical formula by an appropriate integer factor to obtain the molecular formula.