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What mass of natural gas (ch4) must you burn to emit 269 kj of heat? ch4(g)+2o2(g)âco2(g)+2h2o(g)δhârxn=â802.3kj express the mass in grams to three significant figures?

Respuesta :

superman1987
When we have ΔH = - 802.3KJ, Negative charge so we can treat the heat as a product of the reaction as the following:
CH4(g) + 2O2(g) → CO2(g) + 2H2O + 802.3KJ
when the enthalpy change is quoted per mole. and  1mole of CH4 give 802.3KJ
1molCH4→802.3KJ
  ????     ←  269 KJ
So how many moles of CH4 if 269 KJ is generated??
moles of CH4 = 269KJ*1mol / 802 = 0.33 mol
and when we have the molar mass of CH4 = 16, we can get the mass from this formula:
 Mass of CH4 = no of moles* molar mass
                        = 0.33 * 16 = 5.24 g

Answer: The mass of methane gas is 5.36 grams.

Explanation:

We are given:

Energy emitted = 269 kJ

The given chemical equation follows:

[tex]CH_4(g)+2O_2(g)\rightarrow CO2(g)+2H_2O(g);\Delta H_{rxn}=-802.3kJ[/tex]

By Stoichiometry of the reaction:

If 802.3 kJ of heat is emitted by 1 mole of methane

Then, 269 kJ of heat will be emitted by = [tex]\frac{1mol}{802.3kJ}\times 269=0.335mol[/tex] of methane

To calculate the mass from given number of moles, we use the equation:

[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]

Molar mass of methane = 16 g/mol

Moles of methane = 0.335 moles

Putting values in above equation, we get:

[tex]0.335mol=\frac{\text{Mass of methane}}{16g/mol}\\\\\text{Mass of methane}=(0.335mol\times 16g/mol)=5.36g[/tex]

Hence, the mass of methane gas is 5.36 grams.

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