# Question #1d3d1

Jan 26, 2018

x = 7 Solution follows

#### Explanation:

From the formula, we can see that the number of oxygen atoms would be 4 + x. The total mass of this oxygen would then be $16 \times \left(4 + x\right) = 64 + 16 x$

In the same way, the mass of the entire compound can be expressed in terms of x, as

$\left(24.3 + 32.1 + 64.0\right) + x \left(2 + 16\right) = 120.4 + 18 x$

The fraction of the mass that is oxygen is therefore

$\frac{64 + 16 x}{120.4 + 18 x}$

and because we know the oxygen represents 71.4% of the mass, we can write

$\frac{64 + 16 x}{120.4 + 18 x} = 0.714$

Now, solve for x:

$64 + 16 x = \left(120.4 + 18 x\right) \times 0.714$

$64 + 16 x = 85.97 + 12.85 x$

$3.15 x = 21.97$

$x = 6.97$ which we round off to 7