Ch. 6 Ex. 16 - Heat Produced from Complete Combustion of Ethane

The heat of combustion for ethane, [tex]\(C_2H_6\)[/tex], is [tex]\(47.8 \, \text{kJ/g}\)[/tex]. How much heat is produced if 9.65 moles of ethane undergo complete combustion?

[tex]\(\square\)[/tex]
[tex]\(\square \times 10 \, \text{kJ}\)[/tex]



Answer :

Let's go through the problem step by step:

1. Identify Given Values:
- Heat of combustion for ethane ([tex]\( C_2H_6 \)[/tex]) is [tex]\( 47.8 \, \text{kJ/g} \)[/tex].
- Number of moles of ethane is [tex]\( 9.65 \, \text{moles} \)[/tex].
- The molar mass of ethane ([tex]\( C_2H_6 \)[/tex]) is [tex]\( 30.07 \, \text{g/mol} \)[/tex].

2. Calculate the Mass of Ethane:
- To find the mass of ethane, multiply the number of moles by the molar mass:
[tex]\[ \text{mass} \, \text{of} \, \text{ethane} = 9.65 \, \text{moles} \times 30.07 \, \text{g/mol} = 290.18 \, \text{g} \][/tex]

3. Calculate the Heat Produced:
- To determine the heat produced from the combustion, multiply the mass of ethane by the heat of combustion:
[tex]\[ \text{heat} \, \text{produced} = 290.18 \, \text{g} \times 47.8 \, \text{kJ/g} = 13,870.38 \, \text{kJ} \][/tex]

4. Convert the Heat Produced to Scientific Notation:
- Converting 13,870.38 kJ to scientific notation:
[tex]\[ 13,870.38 = 1.39 \times 10^4 \, \text{kJ} \][/tex]

Therefore, the heat produced by the complete combustion of 9.65 moles of ethane, reported in scientific notation, is:
[tex]\[ 1.39 \times 10^4 \, \text{kJ} \][/tex]

In the provided boxes, you would fill in:

- First box: 1.39
- Second box: 4