- Analyze the given moles of magnesium and sulfur: \(0.02\) mol Mg and \(0.02\) mol S.
- Calculate the molar ratio: \(\frac{0.02}{0.02} = 1\).
- Conclude that the ratio of Mg to S is \(1:1\).
- Assign the values to the subscripts in the formula \(Mg_xS_y\): \(x = \boxed{1}\), \(y = \boxed{1}\).
Explanation
- Analyzing the reaction data
The chemical reaction involves magnesium (Mg) and sulfur (S) to form magnesium sulfide (\(Mg_xS_y\)). We are given that \(0.02\) moles of magnesium react with \(0.02\) moles of sulfur, and that magnesium sulfide is the only product formed. We need to determine the ratio of moles of magnesium to sulfur in this compound to find the simplest whole-number values for \(x\) and \(y\).
- Determining the molar ratio
The molar ratio of magnesium to sulfur can be calculated from the given quantities. We have \(0.02\) moles of magnesium and \(0.02\) moles of sulfur. Therefore, the ratio of moles of Mg to moles of S is:
\[\frac{\text{moles of Mg}}{\text{moles of S}} = \frac{0.02}{0.02} = 1\]
This means for every 1 mole of magnesium, there is 1 mole of sulfur reacting. Thus, the ratio of magnesium to sulfur in the product is \(1:1\).
- Finalizing the values for x and y
The formula for the product is \(Mg_xS_y\), where \(x\) and \(y\) represent the lowest whole numbers of the respective elements in the compound. Given our stoichiometric ratio of \(1:1\), we have \(x = 1\) and \(y = 1\). This simplifies to the chemical formula MgS. Thus, the lowest whole numbers are \(x = 1\) and \(y = 1\).
Examples
In chemistry, determining the empirical formula of a compound is essential for understanding its composition. For instance, if you are synthesizing a new material in a laboratory, you measure the masses or moles of reactants that combine to form the final product. By finding the simplest molar ratio, you can derive the chemical formula, which helps in calculating theoretical yields and predicting the material's properties for real-world applications like battery technology or material science. In this case, reacting equal moles of magnesium and sulfur leads to the formula MgS, which is a well-known semiconductor material.