The molar mass of acetone (C3H6O) is 58.08: C=12.01 g/mol *3, H=1.0079 g/mol *6 and O=16.00 g/mol.
We are given the density of acetone: 0.788 g/mL
To determine how many moles of acetone are present in the reaction, we need to take the density of acetone, multiply it by 1, and divide it by 58.08. The “1” represents the amount of moles present in the standard molar mass of “58.08” (basically, 1 mole of acetone has a molar mass of 58.08).
Then multiply that number by the given volume of 179 mL.
0.788 g/mL * (1 mol/58.08 g/mol) * (177) = 2.43 mol C3H6O
The answer to this equation is 2.43. This number represents the number of moles of acetone present in the reaction.
Now that we know how many moles of acetone react, we can return to the question, where they give the standard heat (or enthalpy) of the reaction: Delta_rH^o = -1790 kJ
That is, for every mole of acetone in the reaction, +1790 kJ of heat is released (the prefix “-” indicates an exothermic reaction; -1790 kJ cannot be released, as this would denote an endothermic reaction).
To summarize: 1 mol of acetone releases +1790 kJ. However, we have 2.43 moles of acetone.
The rest of the equation is simple:
2.43 moles of acetone * +1790 kJ/mol = 4350 kJ