Question

For each of the following balanced equations, indicate how many moles of the product could be produced by complete reaction of \(1.00 \mathrm{~g}\) of the reactant indicated in boldface. Indicate clearly the mole ratio used for the conversion. a. \(\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \rightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)\) b. \(\mathrm{CaO}(s)+\mathrm{CO}_{2}(g) \rightarrow \mathrm{CaCO}_{3}(s)\) $$ \text { c. } 4 \mathrm{Na}(s)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{Na}_{2} \mathrm{O}(s) $$ d. \(2 \mathbf{P}(s)+3 C l_{2}(g) \rightarrow 2 \mathrm{PCl}_{3}(l)\)

Short answer

The following are the number of moles of products that could be produced by the complete reaction of 1.00g of the reactants indicated: a. NH4Cl: 0.0588 moles (NH3 used, mole ratio 1:1) b. CaCO3: 0.0179 moles (CaO used, mole ratio 1:1) c. Na2O: 0.0218 moles (Na used, mole ratio 4:2) d. PCl3: 0.0323 moles (P used, mole ratio 2:2)

Step-by-step solution

Calculate the moles of reactant

First, we will calculate the number of moles of NH3 given 1.00 g of NH3. NH3 has a molar mass of approximately 17 g/mol. Number of moles of NH3 = \(\frac{1.00 \ \text{g}}{17 \ \text{g/mol}} = 0.0588 \ \text{moles}\)

Determine mole ratio

In the balanced equation, we see that 1 mole of NH3 reacts with 1 mole of HCl to produce 1 mole of NH4Cl. NH3:HCl:NH4Cl = 1:1:1

Calculate moles of product

Using the mole ratio from the balanced equation, we can now calculate number of moles of NH4Cl produced from 0.0588 moles of NH3. Number of moles of NH4Cl = Number of moles of NH3 = 0.0588 moles b. CaO(s) + CO2(g) -> CaCO3(s)

Calculate the moles of reactant

First, we will calculate the number of moles of CaO given 1.00 g of CaO. CaO has a molar mass of approximately 56 g/mol. Number of moles of CaO = \(\frac{1.00 \ \text{g}}{56 \ \text{g/mol}} = 0.0179 \ \text{moles}\)

Determine mole ratio

In the balanced equation, we see that 1 mole of CaO reacts with 1 mole of CO2 to produce 1 mole of CaCO3. CaO:CO2:CaCO3 = 1:1:1

Calculate moles of product

Using the mole ratio from the balanced equation, we can now calculate number of moles of CaCO3 produced from 0.0179 moles of CaO. Number of moles of CaCO3 = Number of moles of CaO = 0.0179 moles c. 4 Na(s) + O2(g) -> 2 Na2O(s)

Calculate the moles of reactant

First, we will calculate the number of moles of Na given 1.00 g of Na. Na has a molar mass of approximately 23 g/mol. Number of moles of Na = \(\frac{1.00 \ \text{g}}{23 \ \text{g/mol}} = 0.0435 \ \text{moles}\)

Determine mole ratio

In the balanced equation, we see that 4 moles of Na reacts with 1 mole of O2 to produce 2 moles of Na2O. Na:O2:Na2O = 4:1:2

Calculate moles of product

Using the mole ratio from the balanced equation, we can now calculate number of moles of Na2O produced from 0.0435 moles of Na. Number of moles of Na2O = \(\frac{1}{2} *\) Number of moles of Na = \(\frac{1}{2} * 0.0435 \ \text{moles} = 0.0218 \ \text{moles}\) d. 2 P(s) + 3 Cl2(g) -> 2 PCl3(l)

Calculate the moles of reactant

First, we will calculate the number of moles of P given 1.00 g of P. P has a molar mass of approximately 31 g/mol. Number of moles of P = \(\frac{1.00 \ \text{g}}{31 \ \text{g/mol}} = 0.0323 \ \text{moles}\)

Determine mole ratio

In the balanced equation, we see that 2 moles of P reacts with 3 moles of Cl2 to produce 2 moles of PCl3. P:Cl2:PCl3 = 2:3:2

Calculate moles of product

Using the mole ratio from the balanced equation, we can now calculate number of moles of PCl3 produced from 0.0323 moles of P. Number of moles of PCl3 = Number of moles of P = 0.0323 moles

Key concepts

Moles

In chemistry, the mole is a fundamental unit that measures the amount of substance. It acts as a bridge to connect the atomic scale to a human-friendly scale.
Specifically, one mole contains the same number of entities (like atoms, molecules, or ions) as there are in 12 grams of carbon-12, which is Avogadro's number: approximately \(6.022 \times 10^{23}\).
Moles help chemists convey and calculate exact measurements when reactions happen between different substances. For example, to find out how many moles are present in a given mass of a substance, you can use the formula:

• Number of moles = \( \frac{\text{Mass}}{\text{Molar Mass}} \)

Understanding this is crucial in grasping stoichiometry and performing any chemical calculation!

Molar Mass

Molar mass is an essential concept in chemistry that represents the mass of one mole of a given substance. It often helps us connect mass with number of moles in chemical calculations.
It is expressed in grams per mole (g/mol). For individual elements, you can find it on the periodic table, as it typically equals the atomic mass expressed in grams.
For chemical compounds, the molar mass is calculated by summing the molar masses of each element in the compound, multiplied by their respective quantities.
For example, ammonia (\(\text{NH}_3\)) has a molar mass of 17 g/mol (\(14 \, \text{g/mol (N)} + 3 \times 1 \, \text{g/mol (H)} \)). This value helps facilitate calculations, such as converting grams of a substance into moles and vice versa.

Chemical Equations

Chemical equations are representations of chemical reactions. These equations show the reactants, products, and their relationships via symbols and formulas.
Reactants are substances present at the beginning, while products are those formed at the end of the reaction.
The equation illustrates the conservation of mass by having the same number of each type of atom on both sides.

• An essential aspect of chemical equations is balancing them, which adjusts coefficients to ensure this balance holds.
• Take the reaction of ammonia and hydrochloric acid: \(\text{NH}_3(g) + \text{HCl}(g) \rightarrow \text{NH}_4\text{Cl}(s)\). This balanced equation shows that one mole of ammonia reacts with one mole of hydrochloric acid to produce one mole of ammonium chloride.

Such equations provide critical insights for calculating reactant and product amounts during a chemical reaction.

Mole Ratios

Mole ratios are crucial for understanding the quantitative aspects of chemical reactions. They stem from the coefficients in balanced chemical equations.
These ratios allow us to connect the amounts of reactants and products using moles, simplifying predictions about reaction results.
Mole ratios help in answering questions like, "How many moles of one substance will react with another?"
For example, in the reaction: \(2\text{P}(s) + 3\text{Cl}_2(g) \rightarrow 2\text{PCl}_3(l)\), the mole ratio of phosphorus to phosphorus trichloride is 2:2, meaning two moles of phosphorus produce two moles of phosphorus trichloride.
Understanding and utilizing these ratios helps in the conversion and calculation of masses, moles, and volumes in chemical processes.