91Ó°ÊÓ

In every chemical reaction, it's essential to identify which reactant will run out first as it determines how much product can be formed. In the given reaction of \( \mathrm{Ag}^{+} \) with \( \mathrm{CrO}_{4}^{2-} \), the stoichiometry shows us that two moles of \( \mathrm{Ag}^{+} \) are needed to react with one mole of \( \mathrm{CrO}_{4}^{2-} \) to form \( \mathrm{Ag}_{2} \mathrm{CrO}_{4} \).
Since we start with an equal number of moles of \( \mathrm{Ag}^{+} \) and \( \mathrm{CrO}_{4}^{2-} \), \( \mathrm{Ag}^{+} \) becomes the limiting reactant. Why? Because you'd need twice the amount of \( \mathrm{Ag}^{+} \) compared to \( \mathrm{CrO}_{4}^{2-} \) to keep the reaction going. Hence, the amount of \( \mathrm{Ag}_{2} \mathrm{CrO}_{4} \) produced is controlled by the amount of \( \mathrm{Ag}^{+} \) available. Understanding this concept is vital because it not only defines the completion of reactions but also optimizes resource usage in larger-scale productions.

Molar mass is the mass of one mole of a substance and is expressed in grams per mole. It enables the conversion from moles to grams, which is often needed in real-world applications like predicting the mass of a product from a given mass of reactants.
In the exercise, we needed to calculate the molar mass of \( \mathrm{Ag}_{2} \mathrm{CrO}_{4} \). This involves adding up the atomic masses of all atoms that comprise the compound:

• Silver (Ag): Two atoms, each with an atomic mass of 108 \( \mathrm{g/mol} \) contribute a total of \( 216 \mathrm{~g/mol} \).
• Chromium (Cr) contributes \( 52 \mathrm{~g/mol} \).
• Oxygen (O): Four atoms, each with an atomic mass of \( 16 \mathrm{g/mol} \), contribute \( 64 \mathrm{~g/mol} \).

The sum is \( 332 \mathrm{~g/mol} \). Calculating molar masses this way is foundational in chemistry, providing a bridge between molecules and mass.

Chemical equations succinctly represent chemical reactions using symbols and formulas for the elements and compounds involved. They are unbelievably powerful and act like the language of chemistry.
The balanced chemical equation for the reaction between \( \mathrm{Ag}^{+} \) and \( \mathrm{CrO}_{4}^{2-} \) is:
\[\mathrm{2Ag}^{+}(aq) + \mathrm{CrO}_{4}^{2-}(aq) \rightarrow \mathrm{Ag}_{2} \mathrm{CrO}_{4}(s)\]
This balanced equation tells us exactly how reactants combine to form products, showing that every two moles of \( \mathrm{Ag}^{+} \) will produce one mole of \( \mathrm{Ag}_{2} \mathrm{CrO}_{4} \) when reacted with one mole of \( \mathrm{CrO}_{4}^{2-} \). Writing chemical equations is essential for predicting the outcome of chemical reactions and is a fundamental skill throughout chemistry.

Mole conversions are a vital concept for relating the amount of substances to their mass in chemical reactions. A mole is a measure that indicates how many molecules or atoms are present in a substance.
In this exercise, moles conversion is handled by using the molar mass of \( \mathrm{Ag}_{2} \mathrm{CrO}_{4} \). Once the moles of product formed are known, conversions allow us to find out the mass of the \( \mathrm{Ag}_{2} \mathrm{CrO}_{4} \) solid produced.
The formula for mass conversion is:\[\text{mass} = \text{moles} \times \text{molar mass}\]
Plugging in the values, we multiply \( 5.0 \times 10^{-4} \text{ moles} \) by \( 332 \text{ g/mol} \) to find the mass formed: \( 0.166 \text{ g}\). This process is key for translating chemical reactions into results you can measure, useful in laboratories and industry alike.