How much heat (in {kJ}) evolves when 7.0L of C2H2(d = 1.0967kg/m^3) is mixed with a stoichiometric amount of oxygen gas? The combustion reaction is
C2H2+ 5/2 O2-> 2 CO2+ H2O,
Delta H=-1299.5 kJ
Convert 7.0 L to grams. Use density to do that.
Then dH rxn = 1299.5 kJ x (mass C2H2/molar mass C2H2) = ?
To calculate the heat evolved in the combustion of C2H2, we'll need to determine the number of moles of C2H2 and the stoichiometric amount of oxygen required for the reaction. Then we can use the stoichiometry and the enthalpy change (ΔH) to calculate the heat evolved.
Step 1: Determine the number of moles of C2H2
To calculate the number of moles, we need to use the density of C2H2. Density is defined as mass/volume, so we can rearrange the equation to solve for the mass of C2H2:
mass = density × volume
Given:
density of C2H2 (d) = 1.0967 kg/m^3
volume of C2H2 = 7.0 L
First, let's convert 7.0 L to m^3:
1 L = 1/1000 m^3
Therefore, 7.0 L = 7.0/1000 = 0.007 m^3
Now we can calculate the mass of C2H2:
mass = density × volume
mass = 1.0967 kg/m^3 × 0.007 m^3
Step 2: Determine the number of moles of C2H2
Molar mass of C2H2 = 12.01 g/mol + 2 × 1.008 g/mol
Molar mass of C2H2 = 26.04 g/mol
Now we can calculate the number of moles of C2H2:
moles = mass / molar mass
Step 3: Determine the stoichiometric amount of oxygen
The balanced equation tells us that 1 mole of C2H2 reacts with 5/2 moles of O2. Therefore, the stoichiometric amount of O2 required is:
stoichiometric O2 = (5/2) × moles of C2H2
Step 4: Calculate the heat evolved
The heat evolved in the combustion reaction is given by the enthalpy change (ΔH) of the reaction. According to the given information, ΔH = -1299.5 kJ.
Using the stoichiometry of the reaction, we know that 1 mole of C2H2 produces -1299.5 kJ of heat. Therefore, the heat evolved can be calculated using the stoichiometric amount of O2:
heat evolved = ΔH × stoichiometric O2
Substitute the values obtained from previous calculations into the equation to get the final answer.
To calculate the amount of heat evolved during the combustion of C2H2 (acetylene) with oxygen gas, we need to use the given stoichiometry of the reaction and the density of the C2H2 gas. Here's how you can calculate it step by step:
Step 1: Calculate the mass of C2H2.
To calculate the mass of C2H2, we need to use its density and the volume (7.0 L) given in the question. The density of C2H2 is provided as 1.0967 kg/m^3.
Density = Mass / Volume
Mass = Density x Volume
First, we need to convert the volume from liters (L) to cubic meters (m^3):
1 L = 0.001 m^3
Volume in cubic meters (m^3) = 7.0 L x 0.001 m^3/L = 0.007 m^3
Now, we can calculate the mass of C2H2:
Mass = Density x Volume
Mass = 1.0967 kg/m^3 x 0.007 m^3
Step 2: Calculate the moles of C2H2.
To calculate the moles of C2H2, we need to know its molar mass. The molar mass of C2H2 is 26.04 g/mol.
Molar mass of C2H2 = 26.04 g/mol
First, we need to convert the mass of C2H2 from kg to grams:
Mass of C2H2 = Mass x 1000 (convert kg to grams)
Mass of C2H2 = (1.0967 kg/m^3 x 0.007 m^3) x 1000 g/kg
Now, we can calculate the moles of C2H2:
Moles = Mass / Molar mass
Moles = (Mass of C2H2 / Molar mass)
Step 3: Determine the limiting reactant.
The stoichiometry of the reaction tells us that 1 mole of C2H2 reacts with 5/2 moles of O2. The stoichiometric ratio is 1:5/2 = 2:5.
Since the reaction occurs with a stoichiometric amount of oxygen gas, we need to determine the moles of oxygen required to fully react with the calculated moles of C2H2.
Moles of oxygen = (Moles of C2H2) x (5/2)
Step 4: Calculate the heat evolved.
The given enthalpy change for the combustion reaction is -1299.5 kJ. The negative sign indicates that the reaction is exothermic and releases heat.
To calculate the heat evolved, we use the stoichiometric ratio between C2H2 and heat in the balanced equation:
2 moles of C2H2 = -1299.5 kJ
1 mole of C2H2 = -1299.5 kJ / 2
Finally, we can calculate the heat evolved when 7.0L of C2H2 is mixed with a stoichiometric amount of oxygen gas.
Heat evolved = (Moles of C2H2) x (kJ/mole of C2H2)
Heat evolved = (Moles of C2H2) x (-1299.5 kJ / 2)
By following these steps and substituting the values, you can calculate the amount of heat evolved when 7.0L of C2H2 is combusted with a stoichiometric amount of oxygen gas.