# Calculating Molar Mass of Gas [closed]

I am struggling with my work. I am struck with this Question:

Sodium oxalate ($\ce{Na2C2O4}$) decomposes upon heating to produce a gas-phase product.

$0.5000\ \mathrm{g}$ of sodium oxalate is heated and the gaseous product is collected by displacement over water; the final volume of gas collected is $90.7 \ \mathrm{mL}$ and the mass of solid left after this decomposition is $0.3955 \ \mathrm{g}$. If the temperature of the water is $22.4~^\circ\mathrm{C}$ and the atmospheric pressure is $778.3 \ \mathrm{torr}$.

Calculate the molar mass of the gas and determine its molecular formula based on the formula for sodium oxalate.

## closed as off-topic by Todd Minehardt, Jan, Loong♦, Wildcat, jerepierreNov 2 '15 at 16:23

This question appears to be off-topic. The users who voted to close gave this specific reason:

If this question can be reworded to fit the rules in the help center, please edit the question.

• Well, first what is the chemical reaction? – MaxW Nov 2 '15 at 5:48
• This seems like a homework question. We ‎have a policy which states that you should show your thoughts and/or efforts into solving the ‎problem. It'll make us certain that we aren't doing your homework for you. Otherwise, this ‎question may get closed. – bon Nov 2 '15 at 10:13

## 2 Answers

let $M$ be the molar mass of the gas in $\mathrm{g/mol}$. Then by law conservation of mass, the mass of the gas is given as $$m=0.5~\mathrm{g} - 0.3955~\mathrm{g} = 0.1045 ~\mathrm{g}$$
hence, the number of moles of the gas $$n=\frac{m}{M}=\frac{0.1045~\mathrm{g}}{M}$$

Now, using ideal gas equation, $PV=nRT$

Setting the corresponding values, we get $$(778.3\times 133.332~\mathrm{N\cdot m^{-2}})(90.7\times 10^{-6}~\mathrm{m^3})=\frac{0.1045~\mathrm{g}}{M}(8.314~\mathrm{J\cdot mol^{-1} \cdot K^{-1}})((22.4+273.15)~\mathrm{K})$$ I hope you can solve for molar mass $M$ & then determine molecular formula

If we start with .5 g of reactants, we better end up with .5 g of products, or we've done something wrong.

If the mass of the solid left behind is .3955g, then the mass of the gaseous fraction must be 0.5g-0.3955g, or .1045g.

A mole of ideal gas takes up 22.4 l at STP, but we're not at STP. There's a few ways to calculate this, but easiest is P1V1/T1 = P2V2/T2

so 760 torr x 22.4l /273.15 K = 778.3 x V2/295.55 K

This gives the volume of 1 mole of gas at the working temperature. simple division give the number of moles of product. This will give the molar mass, and since the gas can only contain atoms of Na, C, and O, the formula should be evident.