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
