Question

What mass of sodium hydroxide has the same number of oxygen atoms as 100.0 \(\mathrm{g}\) of ammonium carbonate?

Short answer

The mass of sodium hydroxide (NaOH) that has the same number of oxygen atoms as 100.0 g of ammonium carbonate (NH₄)₂CO₃ is 41.6 g.

Step-by-step solution

Find the molecular mass of ammonium carbonate

In order to find the number of moles of ammonium carbonate in the given mass, we need to determine its molecular mass. Ammonium carbonate has a chemical formula of (NH₄)₂CO₃ which means it has 2(NH₄) and 1(CO₃) in a single molecule. Molecular mass of NH₄ = 1 N + 4 H = 14.01 + 4(1.01) = 18.05 g/mol Molecular mass of CO₃ = 1C + 3O = 12.01 + 3(16.00) = 60.01 g/mol Since there are 2(NH₄) and 1(CO₃), the molecular mass of ammonium carbonate is: Molecular mass of (NH₄)₂CO₃ = 2(18.05) + 60.01 = 36.10 + 60.01 = 96.11 g/mol

Calculate the moles of ammonium carbonate and oxygen atoms

Now we will find the moles of ammonium carbonate using the given mass and molecular mass. Moles of ammonium carbonate = Given mass / Molecular mass Moles of ammonium carbonate = 100.0 g / 96.11 g/mol = 1.04 mol Since there is only one oxygen atom (in CO₃) for each ammonium carbonate molecule, the moles of oxygen atoms will also be 1.04 mol.

Find the molecular mass of sodium hydroxide

To calculate the mass of sodium hydroxide (NaOH) that has the same number of moles of oxygen atoms, we need to first find the molecular mass of sodium hydroxide. Molecular mass of NaOH = 1 Na + 1 O + 1 H = 22.99 + 16.00 + 1.01 = 40.00 g/mol

Calculate the mass of sodium hydroxide with the same moles of oxygen atoms

Now we know that we have 1.04 moles of oxygen atoms, and we will find the mass of sodium hydroxide that has the same number of moles of oxygen atoms using its molecular mass: Mass of NaOH = Moles of oxygen atoms x Molecular mass of NaOH Mass of NaOH = 1.04 mol x 40.00 g/mol = 41.6 g Therefore, the mass of sodium hydroxide that has the same number of oxygen atoms as 100.0 g of ammonium carbonate is 41.6 g.

Key concepts

Molecular Mass Calculation

Molecular mass calculation is a fundamental concept in chemistry, essential for converting between mass and moles. Understanding how to calculate molecular mass allows you to determine how much of each element is present in a compound. To do this, we sum the atomic masses of all atoms in a molecule. Each element has a standard atomic mass, usually found on the periodic table. For example, for ammonium carbonate

• The formula is \((NH_4)_2CO_3\).
• Calculate the atomic mass of each element: N = 14.01, H = 1.01, C = 12.01, O = 16.00.
• Add up the masses based on the number of atoms in the formula.

Combine these masses: \(2(NH_4) + 1(CO_3)\) leads to a molecular mass of 96.11 g/mol. Understanding this step ensures you know the precise makeup of a compound, crucial for further calculations.

Moles of Compounds

Moles provide a way to count particles like atoms in chemistry, similar to how dozens work with eggs. To calculate the number of moles in a substance, use the formula:

• \[\text{Moles} = \frac{\text{Given Mass}}{\text{Molecular Mass}}\]

For instance, finding how many moles are in 100.0 g of ammonium carbonate involves dividing by its molecular mass, 96.11 g/mol:

• \[\text{Moles of } (NH_4)_2CO_3 = \frac{100.0 \text{ g}}{96.11 \text{ g/mol}} = 1.04 \text{ mol}\]

This conversion helps determine proportions needed in a chemical reaction or comparison, like the moles of oxygen atoms present in the compound.

Oxygen Atoms

Understanding how oxygen atoms appear in compounds can help figure out their proportions or participate in similar reactions. In our example, ammonium carbonate has one oxygen atom within each \(CO_3\) part. Therefore, the moles of the compound are equal to the moles of oxygen atoms it contains. For sodium hydroxide (NaOH), each molecule also contains a single oxygen atom.

• Ammonium carbonate \(100.0 \text{ g}\): 1.04 mol of \(O\)
• Sodium hydroxide: using its molecular mass of 40.00 g/mol, find an equivalent mass that results in 1.04 mol of \(O\)

Calculate the needed mass for sodium hydroxide:

• \[\text{Mass of NaOH} = 1.04 \text{ mol} \times 40.00 \text{ g/mol} = 41.6 \text{ g}\]

This calculation shows the direct relationship between mole content and mass, emphasizing the oxygen atom's roles across different chemical compounds.