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Answer :
To determine if the two samples are made of the same substance, we can compare the mass ratio of potassium to bromine for each sample. If the ratios are very close or the same, it's likely that they are the same substance.
Step-by-step Solution:
1. Calculate the mass ratio for the first sample:
- For the first sample, we have 7.82 grams of potassium and 16.0 grams of bromine.
- The mass ratio of potassium to bromine is calculated as:
[tex]\[
\text{Ratio}_1 = \frac{\text{mass of potassium}}{\text{mass of bromine}} = \frac{7.82}{16.0} = 0.48875
\][/tex]
2. Calculate the mass ratio for the second sample:
- For the second sample, we have 17.8 grams of potassium and 36.3 grams of bromine.
- The mass ratio of potassium to bromine is calculated as:
[tex]\[
\text{Ratio}_2 = \frac{\text{mass of potassium}}{\text{mass of bromine}} = \frac{17.8}{36.3} \approx 0.49036
\][/tex]
3. Compare the ratios:
- The mass ratio for the first sample is approximately 0.48875.
- The mass ratio for the second sample is approximately 0.49036.
- Since these ratios are not exactly equal and show a slight difference, the samples do not have the same mass ratio of potassium to bromine.
4. Conclusion:
- Since the mass ratios are not the same, the two samples are not made of the same substance. The slight variation in these ratios suggests they have different compositions, or at least are not identical in terms of the proportion of their constituent elements.
Step-by-step Solution:
1. Calculate the mass ratio for the first sample:
- For the first sample, we have 7.82 grams of potassium and 16.0 grams of bromine.
- The mass ratio of potassium to bromine is calculated as:
[tex]\[
\text{Ratio}_1 = \frac{\text{mass of potassium}}{\text{mass of bromine}} = \frac{7.82}{16.0} = 0.48875
\][/tex]
2. Calculate the mass ratio for the second sample:
- For the second sample, we have 17.8 grams of potassium and 36.3 grams of bromine.
- The mass ratio of potassium to bromine is calculated as:
[tex]\[
\text{Ratio}_2 = \frac{\text{mass of potassium}}{\text{mass of bromine}} = \frac{17.8}{36.3} \approx 0.49036
\][/tex]
3. Compare the ratios:
- The mass ratio for the first sample is approximately 0.48875.
- The mass ratio for the second sample is approximately 0.49036.
- Since these ratios are not exactly equal and show a slight difference, the samples do not have the same mass ratio of potassium to bromine.
4. Conclusion:
- Since the mass ratios are not the same, the two samples are not made of the same substance. The slight variation in these ratios suggests they have different compositions, or at least are not identical in terms of the proportion of their constituent elements.
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