[ooooops]

I'm having trouble with starting this question. I have the answers i just don't know how to approach it. Help would be great! 

(the answers are in red)

M is a metal; X is a non-metal. Upon strong heating of 0.5000g of MXO3(s), it
decomposes forming MO(s) and XO2(g). Then, all of the MO(s) was dissolved in water and
excess acid, 100 mL of 0.120M HCl was added. The resulting solution required 40.0 mL
of 0.050 M NaOH for complete neutralization. The rate of effusion of the XO2(g) was
found to be 0.797 times that of N2(g) at the same temperature.
a. Find the number of moles of MO(s) formed.
0.005
b. Identify X.
C
c. Identify M.
Ca

[david.helmly]

X struck me as carbon just because of the "XO2" clause, but it's not really much of a proof, sorry...

...man, I don't know chemistry as well as I thought I did...well, that's the first and most important thing I need to learn!

[Schrödinger]

M is a metal; X is a non-metal. Upon strong heating of 0.5000g of MXO3(s), it
decomposes forming MO(s) and XO2(g). Then, all of the MO(s) was dissolved in water and
excess acid, 100 mL of 0.120M HCl was added. The resulting solution required 40.0 mL
of 0.050 M NaOH for complete neutralization.

HCl reacts with the hydroxide formed by MO upon its reaction with water. Since the metal forms an oxide MO, you would expect it to form M(OH)₂ upon dissolving in water.

Let's start with the NaOH data. NaOH neutralizes the excess acid that is present in the solution. i.e, unused HCl. So you should be able to calculate amount of HCl left unused, and hence the amount of HCl actually used can also be calculated.

Using the previously calculated amount of HCl actually used for reaction with M(OH)₂, you will be able to calculate the atomic mass of M. That gives you the metal Ca.

The rate of effusion of the XO2(g) was
found to be 0.797 times that of N2(g) at the same temperature.

Here you need to use Graham's law of diffusion of gases to find the molecular mass of XO₂.