A propane BBQ combusts propane as shown below:
C3H8 (g) + 5 O2 (g) → 3 CO2 (g) + 4 H2O (l) ΔrH = -2220 kJ/mol
What mass of carbon dioxide (in g) is produced when a BBQ grill releases 129 kJ of heat to its surroundings at constant pressure?
No pork roasts were cooked in the making of this question.
Too bad. I'm ready for pork roasts.
C3H8 (g) + 5 O2 (g) → 3 CO2 (g) + 4 H2O (l) ΔrH = -2220 kJ/mol
We know that 3 moles CO2 are produced from 2220 kJ reaction. 1 mol CO2 = 44 g and 3 mols = 3*44 = 132 g so
132 g CO2 x (129 kJ/2220 kJ) = grams CO2 from 129 kJ of the above reaction of C3H8.
Well, isn't that a sizzling question! Let's fire up the calculations and grill some numbers, shall we?
We know that the reaction releases 2220 kJ/mol. So, to find out how much carbon dioxide (CO2) is produced when 129 kJ of heat is released, we need to do a little mole ratio dance.
First, we need to find the moles of heat released. We'll use the equation:
(129 kJ) / (-2220 kJ/mol) = -0.0581 mol
Since the stoichiometric coefficient of CO2 is 3, we can say that:
-0.0581 mol of CO2 is produced from 1 mol of heat released.
Now, let's convert it to grams. The molar mass of CO2 is approximately 44 g/mol.
(-0.0581 mol CO2) × (44 g/mol) = -2.56 g
Oh no! It seems like something went a little wrong here. Make sure your calculations are positively charged with attention, and try again!
To calculate the mass of carbon dioxide produced, we need to use the given heat released and the molar enthalpy of the reaction.
First, let's calculate the number of moles of heat released:
According to the given information, the molar enthalpy of the reaction is -2220 kJ/mol.
Using the equation:
ΔH = q / n,
where ΔH is the molar enthalpy (kJ/mol), q is the heat released (kJ), and n is the number of moles of reactant or product involved in the reaction.
Let's rearrange the equation to solve for n:
n = q / ΔH.
Substituting the given values:
n = 129 kJ / -2220 kJ/mol.
Now, we can calculate the number of moles of carbon dioxide produced:
n(CO2) = n(C3H8) × (3 moles CO2 / 1 mole C3H8).
Next, we can convert the moles of carbon dioxide to grams using the molar mass of CO2.
The molar mass of CO2 = 12.01 g/mol (C) + 2 * 16.00 g/mol (O) = 44.01 g/mol.
Finally, we can find the mass of carbon dioxide produced:
mass(CO2) = n(CO2) × molar mass(CO2).
Now, let's plug in the values and calculate:
n = 129 kJ / -2220 kJ/mol ≈ -0.05814 mol.
n(CO2) = -0.05814 mol × (3 moles CO2 / 1 mole C3H8) ≈ -0.1744 mol.
mass(CO2) = -0.1744 mol × 44.01 g/mol ≈ -7.67 g.
Since the mass cannot be negative, we can conclude that no carbon dioxide is produced when the barbecue grill releases 129 kJ of heat to its surroundings.
To find the mass of carbon dioxide produced, we need to use the given information about the heat released (ΔrH) and the balanced chemical equation.
Step 1: Calculate the number of moles of heat released
We can use the equation q = ΔrH*n, where q is the heat released, ΔrH is the enthalpy change per mole, and n is the number of moles of the substance involved. Rearranging the equation, we have n = q / ΔrH.
Given that the heat released is 129 kJ and the enthalpy change is -2220 kJ/mol, we can substitute these values into the equation to find the number of moles:
n = 129 kJ / -2220 kJ/mol
Step 2: Use stoichiometry to find the moles of carbon dioxide
Referencing the balanced chemical equation:
C3H8 (g) + 5 O2 (g) → 3 CO2 (g) + 4 H2O (l)
We can see that for every 3 moles of carbon dioxide produced, there are 1 mole of C3H8. Therefore, the number of moles of carbon dioxide is the same as the number of moles of C3H8.
Step 3: Convert moles to grams
To convert moles of carbon dioxide to grams, we will use the molar mass of carbon dioxide, which is 44.01 g/mol.
Finally, the mass of carbon dioxide produced can be calculated by:
Mass of CO2 = Number of moles of CO2 * Molar mass of CO2
Let's calculate it:
Step 1:
n = 129 kJ / -2220 kJ/mol (kJ unit canceled out)
n ≈ -0.0581 mol (rounded to four decimal places)
Step 2:
The number of moles of carbon dioxide produced is also -0.0581 mol.
Step 3:
Mass of CO2 = (-0.0581 mol) * (44.01 g/mol)
Mass of CO2 ≈ -2.55 g (rounded to two decimal places)
Please note that the negative sign in the mass indicates that the reaction is exothermic, meaning heat is released. The magnitude of the mass does not change since the molar mass is always positive. The negative sign simply indicates the direction of the reaction.