74. The equation for the combustion of #CH_4# (the main component of natural gas) is shown below. How much heat is produced by the complete combustion of 237 g of #CH_4#?

#CH_4 (g) + 2O_2 (g) -> CO_2 (g) + 2H_2O (g)#
#DeltaH = -"802.3 kJ/mol"#

Answer 1

#"11900 kJ"#

The problem provides you with the thermochemical equation that describes the combustion of methane, #"CH"_4#
#"CH"_ (4(g)) + 2"O"_ (2(g)) -> "CO"_ (2(g)) + 2"H"_ 2"O"_ ((g))" "DeltaH = - "802.3 kJ mol"^(-1)#
The enthalpy change of combustion, given here as #DeltaH#, tells you how much heat is either absorbed or released by the combustion of one mole of a substance.

In your case, the enthalpy change of combustion

#DeltaH = -"802.3 kJ mol"^(-1)#
suggests that the combustion of one mole of methane gives off, hence the minus sign, #"802.3 kJ"# of heat.

Your strategy here will be to use the molar mass of methane to convert your sample from grams to moles

#237 color(red)(cancel(color(black)("g"))) * "1 mole CH"_4/(16.04color(red)(cancel(color(black)("g")))) = "14.776 moles CH"_4#
Since you know that #1# mole produces #"802.3 kJ"# of heat upon combustion, you can say that #14.776# moles will produce
#14.776 color(red)(cancel(color(black)("moles CH"_4))) * overbrace("802.3 kJ"/(1color(red)(cancel(color(black)("mole CH"_4)))))^(color(blue)(= DeltaH)) = "11854.8 kJ"#

Rounded to three sig figs, the answer will be

#"heat produced" = color(green)(|bar(ul(color(white)(a/a)color(black)("11900 kJ")color(white)(a/a)|)))#
This is equivalent to saying that the enthalpy change of reaction, #DeltaH_"rxn"#, when #"237 g"# of methane undergo combustion is
#DeltaH_"rxn" = -"11900 kJ"#

Keep in mind that the minus sign is used to symbolize heat given off.

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Answer 2

The balanced equation for the combustion of CH4 is:

CH4(g) + 2O2(g) -> CO2(g) + 2H2O(g)

The molar mass of CH4 is approximately 16.04 g/mol. The molar mass of CO2 is approximately 44.01 g/mol. The molar mass of H2O is approximately 18.02 g/mol.

The heat produced by the combustion of 1 mole of CH4 is -802.3 kJ/mol.

To find the heat produced by the combustion of 237 g of CH4, first calculate the number of moles of CH4:

moles of CH4 = mass of CH4 / molar mass of CH4

Then, use the stoichiometry of the balanced equation to find the heat produced:

moles of CH4 * (heat produced per mole of CH4)

Finally, multiply by the appropriate conversion factor to get the heat in the desired units (kJ or J).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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