Using the balanced equation shown below, what is the mass of C3H8 that must react in order to release 1.25×10^6 kJ of heat?
ΔHrxn = –2219.9 kJ

Question

Using the balanced equation shown below, what is the mass of C3H8 that must react in order to release 1.25×10^6  kJ of heat?
ΔHrxn = –2219.9 kJ

Naomi Aronson · Accepted Answer

Well, it seems that

#m_(C_3H_8) = "24.8 kg"#

Since reactions typically happen under continuous pressure, we write that

#q_(rxn) = DeltaH_(rxn)#

I assume your #DeltaH_(rxn)# units are not correct and should be #"kJ/mol"#; otherwise, there would not be any point in knowing the mass of the reactant.

Define #DeltabarH_(rxn) = (DeltaH_(rxn))/n_(C_3H_8)#, where #n_(C_3H_8)# is mols of #"C"_3"H"_8#. This means...

#n_(C_3H_8)DeltabarH_(rxn) = DeltaH_(rxn) = q_(rxn)#

#= n_(C_3H_8) xx (-"2219.9 kJ"/("mol C"_3"H"_8))#

# = -1.25 xx 10^6# #"kJ"#

As a result, this many propane mols reacted:

#n_(C_3H_8) = -1.25 xx 10^6 cancel"kJ" xx ("1 mol C"_3"H"_8)/(-2219.9 cancel"kJ")#

#=# #"563.09 mols"#

Well, in that case... Wow, that's really big.

#color(blue)(m_(C_3H_8)) = 563.09 cancel("mols C"_3"H"_8) xx ("44.1 g C"_3"H"_8)/cancel("1 mol C"_3"H"_8)#

#=# #"24832.20 g C"_3"H"_8#

#= color(blue)("24.8 kg C"_3"H"_8)#

This factory is where I would not want to work—they are burning tons of propane!

Olivia Anton · Answer

undefined To find the mass of $ C_3H_8 $ required to release $ 1.25 \times 10^6 $ kJ of heat, use the equation:

$$
\Delta H_{\text{rxn}} = \text{mass of } C_3H_8 \times \text{heat of combustion per mole}
$$

First, convert the given heat of reaction to kJ/mol by dividing by the number of moles of $ C_3H_8 $ involved in the reaction. Then, rearrange the equation to solve for the mass of $ C_3H_8 $. The balanced equation for the combustion of $ C_3H_8 $ is:

$$
C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O
$$

The heat of combustion per mole of $ C_3H_8 $ is $ \Delta H = -2219.9 $ kJ/mol.

Substituting the given values into the equation:

$$
\Delta H_{\text{rxn}} = \text{mass of } C_3H_8 \times \Delta H
$$

$$
1.25 \times 10^6 \, \text{kJ} = \text{mass of } C_3H_8 \times (-2219.9 \, \text{kJ/mol})
$$

Solve for the mass of $ C_3H_8 $:

$$
\text{mass of } C_3H_8 = \frac{1.25 \times 10^6 \, \text{kJ}}{-2219.9 \, \text{kJ/mol}} \approx 563.51 \, \text{mol}
$$

Therefore, approximately 563.51 grams of $ C_3H_8 $ must react to release $ 1.25 \times 10^6 $ kJ of heat.

Using the balanced equation shown below, what is the mass of C3H8 that must react in order to release 1.25×10^6 kJ of heat? ΔHrxn = –2219.9 kJ