Question

an analytical chemist measures the amount of elements $e_1$ and $e_2$ in four samples of an unknown substance $x$:

sample	mass of $e_1$	mass of $e_2$
2	7.6 g	17.3 g
3	7.0 g	16.1 g
4	4.3 g	9.8 g

its known that $x$ contains no elements other than $e_1$ and $e_2$.
using this information, answer the questions in the table below.
is $x$ a pure substance or a mixture? if you dont have enough information to decide, choose cant decide.
if you said $x$ is a pure substance, calculate the mass of element $e_1$ the analytical chemist would find in a new 10.0 g sample of $x$. round your answer to 2 significant digits.

Explanation:

Step1: Calculate mass - ratio for each sample

For sample 1: $\frac{\text{mass of }E_1}{\text{mass of }E_2}=\frac{7.3}{16.6}\approx0.44$
For sample 2: $\frac{\text{mass of }E_1}{\text{mass of }E_2}=\frac{7.6}{17.3}\approx0.44$
For sample 3: $\frac{\text{mass of }E_1}{\text{mass of }E_2}=\frac{7.0}{16.1}\approx0.43$
For sample 4: $\frac{\text{mass of }E_1}{\text{mass of }E_2}=\frac{4.3}{9.8}\approx0.44$

Since the mass - ratio of $E_1$ to $E_2$ is approximately the same in all samples, $X$ is a pure substance.

Step2: Calculate the fraction of $E_1$ in $X$

The average mass - ratio of $E_1$ to the total mass in the samples:
Let's take the average of the mass - ratios calculated above. The average mass - ratio of $E_1$ to $E_2$ is approximately $0.44$. So the fraction of $E_1$ in $X$ is $\frac{0.44}{1 + 0.44}=\frac{0.44}{1.44}\approx0.3056$.

Step3: Calculate the mass of $E_1$ in a 10.0 g sample of $X$

The mass of $E_1$ in a 10.0 g sample of $X$ is $m = 10.0\times0.3056\approx3.1$ g.

Answer:

Is $X$ a pure substance or a mixture? pure substance
If you said $X$ is a pure substance, calculate the mass of Element $E_1$ the analytical chemist would find in a new 10.0 g sample of $X$. 3.1 g