Problem 172 - Introductory Chemistry Atoms First

Question

Calcium hydroxide reacts with phosphoric acid to produce calcium phosphate and water. (a) How many grams of phosphoric acid are needed to react completely with \(34.6 \mathrm{~g}\) of calcium hydroxide? (b) How many grams of calcium phosphate would theoretically be produced with the masses of part (a)?

Step-by-Step Solution

Answer

a) 30.5 g of phosphoric acid is needed to react completely with 34.6 g of calcium hydroxide. b) 48.1 g of calcium phosphate would theoretically be produced with the masses of part (a).

Step 1: Write the balanced chemical equation

Let's start by writing the balanced chemical equation for the reaction: \(Ca(OH)_2 + H_3PO_4 \rightarrow Ca_3(PO_4)_2 + H_2O\) First, we need to balance this equation: \(3Ca(OH)_2 + 2H_3PO_4 \rightarrow Ca_3(PO_4)_2 + 6H_2O\) Now, we have the balanced equation to work with.

Step 2: Calculate moles of calcium hydroxide

Now, let's convert the given mass of calcium hydroxide (34.6 g) to moles. To do this, we use the molar mass of calcium hydroxide, which is \(74.1 \mathrm{~g/mol}\). Moles of calcium hydroxide = \(\frac{\mathrm{mass}}{\mathrm{molar~mass}} = \frac{34.6\mathrm{~g}}{74.1 \mathrm{~g/mol}} = 0.467\mathrm{~mol}\)

Step 3: Calculate moles and grams of phosphoric acid

Using the balanced equation, we can determine the moles of phosphoric acid needed to react completely with the moles of calcium hydroxide. Here, we can see that for every 3 moles of calcium hydroxide, 2 moles of phosphoric acid are required: Moles of phosphoric acid = \(\Big(\frac{2 \mathrm{~mol~H_3PO_4}}{3 \mathrm{~mol~Ca(OH)_2}}\Big)\times 0.467\mathrm{~mol~Ca(OH)_2} = 0.311\mathrm{~mol~H_3PO_4}\) Now, we need to convert the moles of phosphoric acid to grams. The molar mass of phosphoric acid is \(98.0 \mathrm{~g/mol}\). Mass of phosphoric acid = moles × molar mass = \(0.311\mathrm{~mol~H_3PO_4}\times 98.0 \mathrm{~g/mol} = 30.5\mathrm{~g}\) So, 30.5 g of phosphoric acid is needed to react completely with 34.6 g of calcium hydroxide.

Step 4: Calculate moles and grams of calcium phosphate

Now, let's calculate the moles of calcium phosphate produced according to the balanced equation. For every 3 moles of calcium hydroxide, 1 mole of calcium phosphate is produced: Moles of calcium phosphate = \(\Big(\frac{1 \mathrm{~mol~Ca_3(PO_4)_2}}{3 \mathrm{~mol~Ca(OH)_2}}\Big) \times 0.467\mathrm{~mol~Ca(OH)_2} = 0.155\mathrm{~mol~Ca_3(PO_4)_2}\) Now, let's convert the moles of calcium phosphate to grams. The molar mass of calcium phosphate is \(310.2 \mathrm{~g/mol}\). Mass of calcium phosphate = moles × molar mass = \(0.155\mathrm{~mol~Ca_3(PO_4)_2}\times 310.2\mathrm{~g/mol} = 48.1 \mathrm{~g}\) So, 48.1 g of calcium phosphate would theoretically be produced with the masses of part (a). In summary: a) 30.5 g of phosphoric acid is needed to react completely with 34.6 g of calcium hydroxide. b) 48.1 g of calcium phosphate would theoretically be produced with the masses of part (a).

Key Concepts

Chemical Reaction

A chemical reaction is a process where substances, known as reactants, transform into different substances called products. This transformation occurs through the breaking and forming of chemical bonds. For instance, calcium hydroxide reacts with phosphoric acid to produce calcium phosphate and water. It's a complex dance of atoms that rearrange themselves to create new materials.

This transformation is not random; it follows the laws of conservation of mass and energy. That means during a chemical reaction, the total mass and energy of the reactants equal the total mass and energy of the products. The real-life implications of understanding chemical reactions are vast, ranging from creating new materials to understanding biological processes.

Molar Mass

The molar mass of a substance is the weight of 1 mole (6.022 x 10²³ particles) of that substance, typically expressed in grams per mole (g/mol). The molar mass reflects how much one mole of any given substance weighs and is crucial in converting between the mass of a substance and the amount in moles.

For example, calcium hydroxide has a molar mass of 74.1 g/mol. This value is pivotal because it allows us to convert the given mass of substances into moles, which then allows us to use the balanced chemical equation to relate the amounts of different substances involved in the reaction.

Balanced Chemical Equation

A balanced chemical equation ensures that the number of atoms for each element is the same in the reactants and products, following the law of conservation of mass. The balancing act is a fundamental requirement before any quantity-related calculations can take place in stoichiometry.

In our exercise, the balanced equation 3Ca(OH)₂ + 2H₃PO₄ → Ca₃(PO₄)₂ + 6H₂O communicates not just the species involved, but also their relative quantities, laying the groundwork for mole-based stoichiometric calculations.

Moles to Grams Conversion

Converting from moles to grams is a fundamental operation in stoichiometry that requires the molar mass as a conversion factor. Once we have the amount of a substance in moles, we can easily determine the mass using the equation: Mass (g) = Number of moles × Molar mass (g/mol).

In our example, we used this conversion to find out how many grams of phosphoric acid react with calcium hydroxide, as well as to predict the mass of calcium phosphate produced. Understanding this conversion is crucial in practical chemistry, from tailoring reaction quantities in a lab to industrial synthesis of chemicals, making the moles to grams calculation an indispensable tool for any chemist.