Answered

A 0.405 mol sample of a metal oxide, $X_2O_3$, weighs 60.7 g.



Part 1 of 3:

How many moles of O are in the sample? Be sure your answer has the correct number of significant figures.



Part 2 of 3:

How many grams of X are in the sample? Be sure your answer has the correct number of significant figures.



Part 3 of 3:

Which element is represented by the symbol X? (Give the elemental symbol of that element.)

Verified Answer :

  • Determine the moles of metal \(X\) from the sample quantity: \(0.405 \, \text{mol} \times 2 = 0.810 \, \text{mol}\).
  • Calculate the molar mass of \(X\) using its mass and mole count: \(41.3 \, \text{g} / 0.810 \, \text{mol} \approx 50.99 \, \text{g/mol}\).
  • Identify element \(X\) as Vanadium by comparing its molar mass to the periodic table: \(\boxed{V}\).

Explanation

  1. Analysis of the Sample Composition

To identify the element \(X\) in the metal oxide \(X_2O_3\), we first analyze the composition of the sample. We are given that we have \(0.405 \, \text{mol}\) of \(X_2O_3\) and a total mass of \(60.7 \, \text{g}\). From the chemical formula \(X_2O_3\), we know that for every mole of \(X_2O_3\), there are 2 moles of the metal \(X\) and 3 moles of oxygen \(O\). Using this stoichiometry, we can determine the number of moles of the metal \(X\) present in the sample.

  1. Calculating Moles and Molar Mass of X

Given the sample size of \(0.405 \, \text{mol}\) of \(X_2O_3\), the total number of moles of the metal \(X\) is:
\[\text{Moles of } X = 0.405 \, \text{mol } X_2O_3 \times \frac{2 \, \text{mol } X}{1 \, \text{mol } X_2O_3} = 0.810 \, \text{mol } X.\]
We are also provided with the total mass of the metal \(X\) in the sample, which is \(41.3 \, \text{g}\). With both the mass and the number of moles of \(X\) known, we can calculate the molar mass of the element \(X\).

  1. Identifying Element X

The molar mass of an element is defined as the mass in grams divided by the number of moles:
\[\text{Molar mass of } X = \frac{\text{Mass of } X}{\text{Moles of } X} = \frac{41.3 \, \text{g}}{0.810 \, \text{mol}} \approx 50.99 \, \text{g/mol}.\]
Comparing this calculated molar mass of approximately \(50.99 \, \text{g/mol}\) to the periodic table, we find that the element with an atomic mass closest to \(50.99 \, \text{g/mol}\) is Vanadium (V), which has an atomic mass of approximately \(50.94 \, \text{g/mol}\). Therefore, the element represented by the symbol \(X\) is Vanadium. The elemental symbol is \(\boxed{V}\).

Examples

Determining the identity of an element from the mass and stoichiometry of its compound is a common task in analytical chemistry. For example, if a chemist isolates a pure sample of an unknown mineral containing a specific metal, they can weigh it and use titration or other techniques to find the total moles of that metal. By calculating the molar mass, they can identify the specific metal, which is crucial for confirming the purity of materials used in industry, such as manufacturing high-strength steel alloys where Vanadium is frequently added to improve properties.

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