A 16.48 g sample of potassium permanganate is dissolved in a 250.0 mL volumetric flask. A 125.1 mL sample of the potassium permanganate solution is added to 75.3 mL of 5.110 M hydrobromic acid in which 32.3 mL of ethanol has been dissolved (d = 0.7891 g/mL) in 3.337 L sealed reaction vessel at 22.1ºC and 743 mmHg. What is the pressure of carbon dioxide gas?

To find the pressure of carbon dioxide gas, we can use the Ideal Gas Law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

First, let's calculate the number of moles of carbon dioxide gas. We need to use the balanced chemical equation for the reaction between potassium permanganate (KMnO4) and hydrobromic acid (HBr) to determine the moles of CO2 formed.

The balanced equation is:
2 KMnO4 + 16 HBr -> 2 MnBr2 + 8 H2O + 5 Br2 + CO2

From the equation, we can see that 2 moles of KMnO4 produce 1 mole of CO2.

Given that the sample of potassium permanganate weighs 16.48 g, we can convert this mass to moles using its molar mass. The molar mass of KMnO4 is approximately 158.04 g/mol.
Moles of KMnO4 = Mass / Molar mass
Moles of KMnO4 = 16.48 g / 158.04 g/mol ≈ 0.1043 mol

Since 2 moles of KMnO4 produce 1 mole of CO2, we can calculate the moles of CO2 using the mole ratio:
Moles of CO2 = Moles of KMnO4 / 2
Moles of CO2 = 0.1043 mol / 2 ≈ 0.0521 mol

We are given the volume of the reaction vessel as 3.337 L and the temperature as 22.1°C, which we need to convert to Kelvin by adding 273.15 to it:
Temperature (T) = 22.1°C + 273.15 = 295.25 K

Now, we can substitute the values into the Ideal Gas Law equation:
PV = nRT

Rearranging the equation to solve for P:
P = (nRT) / V

Substituting the values:
P = (0.0521 mol * 0.0821 L·atm/(mol·K) * 295.25 K) / 3.337 L

Calculating P:
P ≈ 1.172 atm

Therefore, the pressure of carbon dioxide gas is approximately 1.172 atm.

To determine the pressure of carbon dioxide gas in the reaction vessel, we first need to calculate the number of moles of carbon dioxide produced.

1. Calculate the number of moles of potassium permanganate:
Molar mass of potassium permanganate (KMnO4) = 158.034 g/mol
Number of moles = Mass / Molar mass
Number of moles of KMnO4 = 16.48 g / 158.034 g/mol

2. Calculate the concentration of the potassium permanganate solution:
Concentration (M) = Number of moles / Volume (L)
Volume of the solution = 250.0 mL = 0.250 L
Concentration of the potassium permanganate solution = Number of moles / 0.250 L

3. Calculate the number of moles of potassium permanganate in the 125.1 mL sample:
Number of moles = Concentration x Volume (L)
Number of moles of KMnO4 in the 125.1 mL sample = Concentration x (125.1 mL / 1000 mL/L)

4. Determine the limiting reactant (the reactant that is completely consumed):
We need to compare the number of moles of potassium permanganate and hydrobromic acid to find the limiting reactant. The balanced chemical equation is needed for this step.

The balanced chemical equation for the reaction between potassium permanganate (KMnO4) and hydrobromic acid (HBr) is:
2 KMnO4 + 16 HBr -> 2 MnBr2 + 8 H2O + 5 Br2

Based on the balanced equation, we can see that the stoichiometric ratio between KMnO4 and Br2 is 2:5.

Comparing the moles of KMnO4 and HBr using their stoichiometric ratio, we can determine which reactant is limiting.

5. Calculate the number of moles of hydrobromic acid:
Concentration of HBr = 5.110 M
Volume of HBr solution = 75.3 mL = 0.0753 L
Number of moles of HBr = Concentration x Volume (L)

6. Determine the limiting reactant:
Compare the moles of KMnO4 and HBr using their stoichiometric ratio. The reactant with the lower number of moles is the limiting reactant.

7. Calculate the number of moles of carbon dioxide produced:
Using the stoichiometric ratio from the balanced equation, which is 2 KMnO4 : 5 CO2, determine the number of moles of carbon dioxide produced.

8. Calculate the total number of moles of carbon dioxide:
Since we now know the number of moles of carbon dioxide produced, we need to determine the total number of moles. We need to consider the moles of carbon dioxide produced from the limiting reactant and the excess reactant.

9. Calculate the partial pressure of carbon dioxide:
Partial pressure of carbon dioxide = (Number of moles of carbon dioxide / Total number of moles) x Total pressure

Given that the total pressure is 743 mmHg, substitute the values into the equation to find the pressure of carbon dioxide gas.