# Question 049d8

Oct 8, 2017

15.5 grams

#### Explanation:

The ratio of x to y is 3:4. Since we know how many atoms of y there are, we can set up a proportion:

$\frac{3}{4} \cdot \frac{x}{3.2 \cdot {10}^{23} \text{ atoms of y}}$

x = ((3.2*10^23 " atoms of y") * 3) / 4 = 2.4 * 10^23 " atoms of x"

Next, we convert the value we just found into moles:

$2.4 \cdot {10}^{23} \text{ atoms of x" * (1 " mole")/(6.022 * 10^23 " atoms") = 0.3985 " moles of x}$

We know how many grams of x there are, so with the help of a little dimensional analysis, we can find the amount of grams

$\left(18.5 \text{ grams of x")/(0.3985 " moles of x}\right) = 46.424$ $\text{grams"/"mole}$

Next, we need to divide this value by three, since there are three atoms of x per every four atoms of y. In another words, the molecular formula given looks something like this: ${N}_{x} {O}_{y}$. Disregard, the N and O in that molecular formula - it's merely an example. We found the molar mass of ${N}_{x}$ but we need the molar mass of $N$.

(46.424 "grams"/"mole")/ 3" = 15.5# $\text{grams"/"mole}$

The element closest to that value of atomic weight is Oxygen, which has a molar mass of 15.9994 grams.