Questions: An analytical chemist measures the amount of Elements E₁ and E₂ in four samples of an unknown Substance X: sample mass of E₁ mass of E₂ -------------------------------- 1 7.5 g 25.4 g 2 5.9 g 20.1 g 3 4.3 g 14.6 g 4 5.6 g 19.3 g It's known that X contains no elements other than E₁ and E₂. Using this information, answer the questions in the table below. Question Answer -------------------------------------------------------------------------------------------------------------------------------------------------- Is X a pure substance or a mixture? If you don't have enough information to decide, choose can't decide. pure substance mixture (can't decide) If you said X is a pure substance, calculate the mass of element E₁ the analytical chemist would find in a new 10.0 g sample of X. Round your answer to 2 significant digits. □ g

An analytical chemist measures the amount of Elements E₁ and E₂ in four samples of an unknown Substance X:

 sample  mass of E₁  mass of E₂ 
--------------------------------
 1       7.5 g       25.4 g     
 2       5.9 g       20.1 g     
 3       4.3 g       14.6 g     
 4       5.6 g       19.3 g     

It's known that X contains no elements other than E₁ and E₂.

Using this information, answer the questions in the table below.

 Question                                                                                                                    Answer               
--------------------------------------------------------------------------------------------------------------------------------------------------
 Is X a pure substance or a mixture? If you don't have enough information to decide, choose can't decide.                    pure substance mixture (can't decide) 
 If you said X is a pure substance, calculate the mass of element E₁ the analytical chemist would find in a new 10.0 g sample of X. Round your answer to 2 significant digits.  □ g
Transcript text: An analytical chemist measures the amount of Elements $E_{1}$ and $E_{2}$ in four samples of an unknown Substance $X$ : \begin{tabular}{|c|c|c|} \hline sample & \begin{tabular}{c} mass \\ of $E_{1}$ \end{tabular} & \begin{tabular}{l} mass \\ of $E_{2}$ \end{tabular} \\ \hline 1 & 7.5 g & 25.4 g \\ \hline 2 & 5.9 g & 20.1 g \\ \hline 3 & 4.3 g & 14.6 g \\ \hline 4 & 5.6 g & 19.3 g \\ \hline \end{tabular} It's known that $X$ contains no elements other than $E_{1}$ and $E_{2}$. Using this information, answer the questions in the table below. \begin{tabular}{|c|c|} \hline \begin{tabular}{l} Is $X$ a pure substance or a mixture? \\ If you don't have enough information to decide, choose can't decide. \end{tabular} & \begin{tabular}{l} pure substance \\ mixture \\ (can't decide) \end{tabular} \\ \hline \begin{tabular}{l} 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. \end{tabular} & $\square \mathrm{g}$ \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Determine if $X$ is a pure substance or a mixture

To determine if $X$ is a pure substance or a mixture, we need to check if the ratio of the masses of $E_1$ to $E_2$ is constant across all samples.

Calculate the ratio for each sample:

  • Sample 1: \(\frac{7.5 \, \text{g}}{25.4 \, \text{g}} = 0.2953\)
  • Sample 2: \(\frac{5.9 \, \text{g}}{20.1 \, \text{g}} = 0.2935\)
  • Sample 3: \(\frac{4.3 \, \text{g}}{14.6 \, \text{g}} = 0.2945\)
  • Sample 4: \(\frac{5.6 \, \text{g}}{19.3 \, \text{g}} = 0.2902\)

The ratios are not exactly the same, but they are very close. This suggests that $X$ is likely a mixture, as a pure substance would have a constant ratio.

Step 2: Conclusion on the nature of $X$

Based on the calculated ratios, we conclude that $X$ is a mixture.

\(\boxed{\text{mixture}}\)

Final Answer

\(\boxed{\text{mixture}}\)

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