Let's analyze the data given for the four samples of substance [tex]\( X \)[/tex].
First, we calculate the total mass for each sample.
1. Sample 1: 11.5 g [tex]\( E_1 \)[/tex] + 6.6 g [tex]\( E_2 \)[/tex] = 18.1 g
2. Sample 2: 17.7 g [tex]\( E_1 \)[/tex] + 10.2 g [tex]\( E_2 \)[/tex] = 27.9 g
3. Sample 3: 15.9 g [tex]\( E_1 \)[/tex] + 9.1 g [tex]\( E_2 \)[/tex] = 25.0 g
4. Sample 4: 18.5 g [tex]\( E_1 \)[/tex] + 10.5 g [tex]\( E_2 \)[/tex] = 29.0 g
Thus, the total masses for the samples are [18.1 g, 27.9 g, 25.0 g, 29.0 g].
Next, we calculate the ratio of [tex]\( E_1 \)[/tex] and [tex]\( E_2 \)[/tex] to the total mass for each sample:
- Ratios of [tex]\( E_1 \)[/tex]:
[tex]\[ \frac{11.5}{18.1} \approx 0.635 \][/tex]
[tex]\[ \frac{17.7}{27.9} \approx 0.634 \][/tex]
[tex]\[ \frac{15.9}{25.0} \approx 0.636 \][/tex]
[tex]\[ \frac{18.5}{29.0} \approx 0.638 \][/tex]
- Ratios of [tex]\( E_2 \)[/tex]:
[tex]\[ \frac{6.6}{18.1} \approx 0.365 \][/tex]
[tex]\[ \frac{10.2}{27.9} \approx 0.366 \][/tex]
[tex]\[ \frac{9.1}{25.0} \approx 0.364 \][/tex]
[tex]\[ \frac{10.5}{29.0} \approx 0.362 \][/tex]
The ratios for [tex]\( E_1 \)[/tex] are approximately [0.635, 0.634, 0.636, 0.638].
The ratios for [tex]\( E_2 \)[/tex] are approximately [0.365, 0.366, 0.364, 0.362].
Since the ratios of [tex]\( E_1 \)[/tex] and [tex]\( E_2 \)[/tex] are not exactly the same across all samples (i.e., there is variability in the ratios), it indicates that [tex]\( X \)[/tex] is likely a mixture and not a pure substance.
Thus, the substance [tex]\( X \)[/tex] is a mixture.
We cannot calculate the mass of [tex]\( E_1 \)[/tex] in a new 10.0 g sample of [tex]\( X \)[/tex] with high confidence because [tex]\( X \)[/tex] is not a pure substance. Therefore, the answer to the mass calculation is "can't decide."
Summary:
- Is [tex]\( X \)[/tex] a pure substance or a mixture? mixture
- If you said [tex]\( X \)[/tex] is a pure substance, calculate the mass of Element [tex]\( E_1 \)[/tex] in a new 10.0 g sample of [tex]\( X \)[/tex]. can't decide
