Nitroglycerin, an explosive compound, decomposes according to the equation below.
4 C3H5(NO3)3(s) 12 CO2(g) + 10 H2O(g) + 6 N2(g) + O2(g)
Calculate the total volume of gases when collected at 1.2 atm and 25°C from 1.3 multiplied by 102 g of nitroglycerin.
What are the partial pressures of the gases under these conditions?
Convert g nitroglycerin to moles. moles = grams/molar mass.
Using the coefficients in the balanced equation, convert moles nitroglycerin to
a. moles CO2
b. moles H2O
c. moles N2
d. moles O2
Add all moles to get a total moles, then use PV = nRT to calculate total volume of all the gases.
Then use PV = nRT to calculate partial pressure of each gas. Use n for each gas, total V, R, an T.
Check my thinking.
To calculate the partial pressures of the gases, we first need to determine the number of moles of each gas produced during the decomposition of 1.3 x 10^2 g of nitroglycerin.
Step 1: Convert the mass of nitroglycerin to moles.
The molar mass of nitroglycerin (C3H5(NO3)3) can be calculated as follows:
C = 12.01 g/mol
H = 1.01 g/mol
N = 14.01 g/mol
O = 16.00 g/mol
Molar Mass of C3H5(NO3)3:
(3 x 12.01 g/mol) + (5 x 1.01 g/mol) + (3 x (14.01 g/mol + 3 x 16.00 g/mol))
= 227.08 g/mol
Number of moles of nitroglycerin:
moles = mass / molar mass
moles = (1.3 x 10^2 g) / (227.08 g/mol)
moles ≈ 0.5723 mol
Step 2: Use the stoichiometry of the balanced equation to determine the moles of each gas produced.
According to the balanced equation, for every 4 moles of nitroglycerin, we get 12 moles of CO2, 10 moles of H2O, 6 moles of N2, and 1 mole of O2.
Number of moles of CO2:
moles of CO2 = (0.5723 mol nitroglycerin) * (12 mol CO2 / 4 mol nitroglycerin)
moles of CO2 ≈ 1.7169 mol
Number of moles of H2O:
moles of H2O = (0.5723 mol nitroglycerin) * (10 mol H2O / 4 mol nitroglycerin)
moles of H2O ≈ 1.4307 mol
Number of moles of N2:
moles of N2 = (0.5723 mol nitroglycerin) * (6 mol N2 / 4 mol nitroglycerin)
moles of N2 ≈ 0.8584 mol
Number of moles of O2:
moles of O2 = (0.5723 mol nitroglycerin) * (1 mol O2 / 4 mol nitroglycerin)
moles of O2 ≈ 0.1436 mol
Step 3: Calculate the partial pressures of the gases.
To calculate the partial pressures, we'll use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
Given that the gases are collected at 1.2 atm and 25°C (which is 298 K), we can substitute these values into the equation to calculate the volume of each gas.
Partial pressure of CO2:
P_CO2 = (n_CO2 * R * T) / V
P_CO2 = (1.7169 mol * 0.0821 L·atm/(mol·K) * 298 K) / V
Partial pressure of H2O:
P_H2O = (n_H2O * R * T) / V
P_H2O = (1.4307 mol * 0.0821 L·atm/(mol·K) * 298 K) / V
Partial pressure of N2:
P_N2 = (n_N2 * R * T) / V
P_N2 = (0.8584 mol * 0.0821 L·atm/(mol·K) * 298 K) / V
Partial pressure of O2:
P_O2 = (n_O2 * R * T) / V
P_O2 = (0.1436 mol * 0.0821 L·atm/(mol·K) * 298 K) / V
Note: The volume (V) of the gases is not given, so we cannot determine the actual partial pressures without it. However, we can provide the partial pressure expressions.
Partial pressure of CO2 = (1.7169 * 0.0821 * 298) / V atm
Partial pressure of H2O = (1.4307 * 0.0821 * 298) / V atm
Partial pressure of N2 = (0.8584 * 0.0821 * 298) / V atm
Partial pressure of O2 = (0.1436 * 0.0821 * 298) / V atm
To calculate the total volume of gases and the partial pressures, we can use the Ideal Gas Law equation, which states:
PV = nRT
Where:
P is the pressure (in atmospheres),
V is the volume (in liters),
n is the number of moles of gas,
R is the ideal gas constant (0.0821 L·atm/(mol·K)),
and T is the temperature (in Kelvin).
First, we need to determine the number of moles of each gas produced in the reaction. Looking at the balanced equation, we can see that 4 moles of nitroglycerin produce 12 moles of carbon dioxide (CO2), 10 moles of water (H2O), 6 moles of nitrogen gas (N2), and 1 mole of oxygen gas (O2).
The molar mass of nitroglycerin (C3H5(NO3)3) can be calculated using the atomic masses of its constituent elements:
C: 12.01 g/mol
H: 1.01 g/mol
N: 14.01 g/mol
O: 16.00 g/mol
Molar mass of nitroglycerin = (3 * 12.01 g/mol) + (5 * 1.01 g/mol) + (3 * 14.01 g/mol) + (9 * 16.00 g/mol) = 227.06 g/mol
Now, we can calculate the number of moles of nitroglycerin:
Moles of nitroglycerin = mass / molar mass
Moles of nitroglycerin = (1.3 * 10^2 g) / (227.06 g/mol) = 0.572 mol
According to the stoichiometry of the balanced equation, we know that each mole of nitroglycerin produces 12 moles of CO2, 10 moles of H2O, 6 moles of N2, and 1 mole of O2.
Moles of CO2 = 0.572 mol * 12 = 6.864 mol
Moles of H2O = 0.572 mol * 10 = 5.720 mol
Moles of N2 = 0.572 mol * 6 = 3.432 mol
Moles of O2 = 0.572 mol * 1 = 0.572 mol
Next, we can calculate the partial pressures of the gases using the Ideal Gas Law equation.
For carbon dioxide (CO2):
P_CO2 = (n_CO2 * R * T) / V
Substituting the values:
P_CO2 = (6.864 mol * 0.0821 L·atm/(mol·K) * 298 K) / V
Now, for water (H2O):
P_H2O = (n_H2O * R * T) / V
Substituting the values:
P_H2O = (5.720 mol * 0.0821 L·atm/(mol·K) * 298 K) / V
For nitrogen gas (N2):
P_N2 = (n_N2 * R * T) / V
Substituting the values:
P_N2 = (3.432 mol * 0.0821 L·atm/(mol·K) * 298 K) / V
For oxygen gas (O2):
P_O2 = (n_O2 * R * T) / V
Substituting the values:
P_O2 = (0.572 mol * 0.0821 L·atm/(mol·K) * 298 K) / V
Finally, we know that the total pressure (P) is given as 1.2 atm. Therefore, the sum of the partial pressures should be equal to the total pressure:
P_CO2 + P_H2O + P_N2 + P_O2 = 1.2 atm
To find the total volume (V) of gases produced, we need to solve these equations simultaneously. This can be done iteratively by substituting the values of P_CO2, P_H2O, P_N2, and P_O2 into the equation.
You can solve these equations using an iterative approach, starting with an initial guess for the volume (V). You can iterate until the sum of the partial pressures reaches 1.2 atm.
Alternatively, you can use a spreadsheet or a numerical analysis software program (e.g., Excel or MATLAB) to solve these equations by setting up a system of equations.
I hope this explanation helps you understand the process of calculating the partial pressures and total volume of gases produced from the given reaction.