Does more volume mean that an object has a higher density

No.

Explanation:

More volume would tend to decrease density. More density can be gotten by increasing the amount of mass per unit of volume.

The reaction for the formation of MgO(s):

2 Mg (s) + O2(g) -à 2MgO(s)                     ΔH = -601.24 kJ/mol

The enthalpy information is taken from: http://webbook.nist.gov/cgi/inchi?ID=C1309484&Mask=2

From the equation and with an enthalpy change of -231 kJ:

-231 kJ * 2 mol Mg * (1/-601.24 kJ/mol) = 0.76841 mol Mg

Then, with the molar mass of MgO = 40.3,

0.76841 mol Mg *(2 mol MgO/2 mol Mg)* 40.3 g/mol MgO = 30.967 g MgO