Question

Given the chemical equation \(\mathrm{Na}_{2} \mathrm{CO}_{3}(a q)+\mathrm{Ca}(\mathrm{OH})_{2}\) \(\longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{CaCO}_{3}(s),\) determine to two decimal places the molar masses of all substances involved. Then, write the molar masses as conversion factors.

Short answer

Molar masses: \( \text{Na}_2\text{CO}_3 = 105.99 \text{ g/mol}, \text{Ca(OH)}_2 = 74.10 \text{ g/mol}, \text{NaOH} = 40.00 \text{ g/mol}, \text{CaCO}_3 = 100.09 \text{ g/mol} \).

Step-by-step solution

- Determine Molar Mass of \(\text{Na}_2\text{CO}_3\)

Calculate the molar mass by summing the atomic masses of all atoms in \(\text{Na}_2\text{CO}_3\):\(2 \times 22.99 + 12.01 + 3 \times 16.00 = 105.99 \) g/mol.

- Determine Molar Mass of \(\text{Ca(OH)}_2\)

Calculate the molar mass by summing the atomic masses of all atoms in \(\text{Ca(OH)}_2\):\(40.08 + 2 \times (16.00 + 1.01) = 74.10 \) g/mol.

- Determine Molar Mass of \(\text{NaOH}\)

Calculate the molar mass by summing the atomic masses of all atoms in \(\text{NaOH}\):\(22.99 + 16.00 + 1.01 = 40.00 \) g/mol.

- Determine Molar Mass of \(\text{CaCO}_3\)

Calculate the molar mass by summing the atomic masses of all atoms in \(\text{CaCO}_3\):\(40.08 + 12.01 + 3 \times 16.00 = 100.09 \) g/mol.

- Convert Molar Masses to Conversion Factors

Write each molar mass as a conversion factor:\(\text{For }\text{Na}_2\text{CO}_3: 1 \text{ mol Na}_2\text{CO}_3 = 105.99 \text{ g Na}_2\text{CO}_3\)\(\text{For }\text{Ca(OH)}_2: 1 \text{ mol Ca(OH)}_2 = 74.10 \text{ g Ca(OH)}_2\)\(\text{For }\text{NaOH}: 1 \text{ mol NaOH} = 40.00 \text{ g NaOH}\)\(\text{For }\text{CaCO}_3: 1 \text{ mol CaCO}_3 = 100.09 \text{ g CaCO}_3\)

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in chemical reactions. It helps us calculate how much of one substance is needed to react with another or how much product will be formed in a reaction.
This is crucial for tasks like determining the molar masses of substances involved in a chemical equation. For the reaction: \(\text{Na}_2\text{CO}_3(aq) + \text{Ca(OH)}_2 \rightarrow 2 \text{NaOH}(aq) + \text{CaCO}_3(s)\), we use stoichiometry to find out how much of each substance we need or will produce.

Molar Mass

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). To find the molar mass of a compound, you sum the atomic masses of all the atoms in the molecule.
For example, for \(\text{Na}_2\text{CO}_3\), you add the masses of 2 sodium atoms, 1 carbon atom, and 3 oxygen atoms together: \(2 \times 22.99\text{ g/mol} + 12.01\text{ g/mol} + 3 \times 16.00\text{ g/mol} = 105.99\text{ g/mol}\). Similar calculations are done for other substances like \(\text{Ca(OH)}_2, \text{NaOH},\) and \( \text{CaCO}_3\).

Conversion Factors

Conversion factors are used to convert quantities from one unit to another. When dealing with chemical reactions, it's often necessary to convert between grams and moles.
For instance, if you know the molar mass of \(\text{Na}_2\text{CO}_3\) is 105.99 g/mol, you can write the conversion factor as:
\(1 \text{ mol Na}_2\text{CO}_3 = 105.99 \text{ g Na}_2\text{CO}_3\).
This helps convert grams of a substance to moles or vice versa, which is essential for precise measurements in reactions.

Chemical Equations

Chemical equations represent chemical reactions where the reactants are transformed into products. They follow the principle of conservation of mass, meaning the mass of the reactants equals the mass of the products.
The given chemical equation is: \(\text{Na}_2\text{CO}_3(aq) + \text{Ca(OH)}_2 \rightarrow 2\text{ NaOH}(aq) + \text{CaCO}_3(s)\).
To balance and interpret these equations correctly, understanding the molar masses and stoichiometric relationships is crucial. Each term in the equation must be accurately accounted to ensure adherence to the conservation laws.