Nitroglycerin is a shock-sensitive liquid that detonates by the reaction
4C3H5(NO3)3(ℓ)-> 6N2(g)+10H2O(g)+12CO2(g)+O2(g)
Calculate the total volume of product gases at 201 kPa and 273 degrees C from the detonation of 3.3 lb (1496.9 g) of nitroglycerin.
Answer in units of L
See your post on stoichiometry and solve with that process. When you find mols of each product, add together, use PV = nRT to solve for volume under the conditions listed.
To calculate the total volume of product gases, we first need to determine the number of moles of each product formed in the reaction. Once we have the moles, we can use the ideal gas law to calculate the volume.
Let's start by converting the mass of nitroglycerin from pounds to grams, and then calculate the number of moles of nitroglycerin using its molar mass.
1 lb = 453.592 g
Mass of nitroglycerin = 3.3 lb = 3.3 * 453.592 g = 1496.9 g
Next, we need to calculate the number of moles of nitroglycerin:
Molar mass of nitroglycerin = (3 * molar mass of carbon) + (5 * molar mass of hydrogen) + (9 * molar mass of oxygen) + 3 * molar mass of nitrogen
Using the atomic masses:
Molar mass of carbon (C) = 12.01 g/mol
Molar mass of hydrogen (H) = 1.01 g/mol
Molar mass of oxygen (O) = 16.00 g/mol
Molar mass of nitrogen (N) = 14.01 g/mol
Molar mass of nitroglycerin = (3 * 12.01) + (5 * 1.01) + (9 * 16.00) + (3 * 14.01) = 227.09 g/mol
Number of moles of nitroglycerin = Mass / Molar mass
Number of moles of nitroglycerin = 1496.9 g / 227.09 g/mol
Now that we have the number of moles of nitroglycerin, we can determine the number of moles of each product formed in the reaction. By comparing the balanced equation, we can see that for every mole of nitroglycerin, we get 6 moles of N2 gas, 10 moles of H2O gas, 12 moles of CO2 gas, and 1 mole of O2 gas.
Number of moles of N2 = Number of moles of nitroglycerin * (6 moles N2 / 1 mole nitroglycerin)
Number of moles of H2O = Number of moles of nitroglycerin * (10 moles H2O / 1 mole nitroglycerin)
Number of moles of CO2 = Number of moles of nitroglycerin * (12 moles CO2 / 1 mole nitroglycerin)
Number of moles of O2 = Number of moles of nitroglycerin * (1 mole O2 / 1 mole nitroglycerin)
Now that we have the number of moles of each product, we can use the ideal gas law to calculate the volume of each gas.
The ideal gas law equation is: PV = nRT
Where:
P = pressure in Pascal (Pa)
V = volume in m^3
n = number of moles
R = ideal gas constant = 8.314 J/(mol K)
T = temperature in Kelvin (K)
In this case, we are given the pressure (201 kPa) and temperature (273°C = 546 K). We need to convert kPa to Pa and Celsius to Kelvin.
Pressure = 201 kPa = 201,000 Pa
Temperature = (273 + 546) K = 819 K
Now we can calculate the volume of each gas using the ideal gas law:
Volume of N2 (V_N2) = (Number of moles of N2 * R * Temperature) / Pressure
Volume of H2O (V_H2O) = (Number of moles of H2O * R * Temperature) / Pressure
Volume of CO2 (V_CO2) = (Number of moles of CO2 * R * Temperature) / Pressure
Volume of O2 (V_O2) = (Number of moles of O2 * R * Temperature) / Pressure
Finally, we can calculate the total volume of product gases by summing up the volumes of each gas:
Total volume = Volume of N2 + Volume of H2O + Volume of CO2 + Volume of O2
Calculating the values will give you the total volume of product gases in liters.