Question

Calculate the moles of the following substances. (a) \(72.2 \mathrm{~g} \mathrm{~K}_{2} \mathrm{SO}_{4}\) (c) \(2.82 \mathrm{~kg}\) magnetite, \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) (b) \(160.0 \mathrm{mg}\) oxycodone, (d) \(5.00 \mu \mathrm{g}\) sucrose, \(\mathrm{C}_{18} \mathrm{H}_{21} \mathrm{NO}_{4}\) \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\)

Short answer

Moles of \(K_{2}SO_{4}\) : 0.4145, Moles of \(Fe_{3}O_{4}\): 12.18, Moles of oxycodone: 0.0005071, Moles of sucrose: \(1.460 \times 10^{-8}\)

Step-by-step solution

Preparation

To calculate the number of moles, the formula used is: \[ \text{Moles} = \frac{\text{mass (g)}}{\text{Molar mass (g/mol)}} \] You need to know the molecular weights of the substances in order to calculate the molar mass. For the first substance (\(K_{2}SO_{4}\)), the molecular weight is 174.259 g/mol, for \(Fe_{3}O_{4}\) it's 231.533 g/mol, for oxycodone it's 315.361 g/mol, and for sucrose, it's 342.296 g/mol.

Calculating moles of \(K_{2}SO_{4}\)

Substitute the given values into the formula. Moles of \(K_{2}SO_{4}\) = \(\frac{72.2g}{174.259 g/mol} = 0.4145 \text{ moles}\)

Calculating moles of \(Fe_{3}O_{4}\)

Convert the given mass from kg to g (since the molar mass is given in g/mol). So, \(2.82 kg = 2820g\), then substitute in the formula. Moles of \(Fe_{3}O_{4}\) = \(\frac{2820g}{231.533 g/mol} = 12.18 \text{ moles}\)

Calculating moles of oxycodone

Convert the given mass from mg to g, so \(160.0 mg = 0.16g\) then substitute in the formula. Moles of oxycodone = \(\frac{0.16g}{315.361 g/mol} = 0.0005071 \text{ moles}\)

Calculating moles of sucrose

Convert the given mass from µg to g, so \(5.00 µg = 0.000005g\) then substitute in the formula. Moles of sucrose = \(\frac{0.000005g}{342.296 g/mol} = 1.460 \times 10^{-8} \text{ moles}\)

Key concepts

Molar Mass

Molar mass is an essential concept in chemistry that plays a crucial role in mole calculations. It's 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 add up the atomic masses of all the elements in the compound. These atomic masses can be found on the periodic table.
For the compound potassium sulfate (\(K_2SO_4\)), the molar mass is calculated as follows:

• Potassium has an atomic mass of 39.098 g/mol.
• Sulfur has an atomic mass of 32.065 g/mol.
• Oxygen has an atomic mass of 15.999 g/mol.

Thus, the molar mass of \(K_2SO_4\) is \((2 \times 39.098) + 32.065 + (4 \times 15.999) = 174.259\) g/mol.
Knowing how to calculate molar mass is crucial when converting between mass and moles, letting you bridge the gap between the macroscopic world of grams and the microscopic world of moles.

Stoichiometry

Stoichiometry is like a recipe for chemical reactions. Just as a cooking recipe tells you the amount of each ingredient needed, stoichiometry provides the ratios of each substance involved in a chemical reaction.
Once you know the amount of one substance (in moles), stoichiometry allows you to calculate the required amounts of other substances.
Using the balanced chemical equation, stoichiometry helps you understand the proportions, making it easier to predict amounts of products or reactants.

• To predict quantities, balance the chemical equation first.
• Convert masses to moles using molar mass.
• Use the balanced equation to set up mole ratios.
• Calculate the desired amount using these ratios.

This method is central to understanding reactant-product relationships and is widely used in laboratory settings.

Molecular Weight

Molecular weight, often synonymous with molar mass, represents the weight of a molecule in atomic mass units (amu). However, when discussing mole calculations, it is expressed in grams per mole (g/mol).
Each element's contribution is based on its atomic mass, as seen in the periodic table.
For compounds like sucrose (\(C_{12}H_{22}O_{11}\)), here's how you calculate the molecular weight:

• Carbon's atomic mass is 12.011 g/mol, multiplied by 12.
• Hydrogen's atomic mass is 1.008 g/mol, multiplied by 22.
• Oxygen's atomic mass is 15.999 g/mol, multiplied by 11.

Add these values to get the molecular weight of sucrose as \((12 \times 12.011) + (22 \times 1.008) + (11 \times 15.999) = 342.296\) g/mol.
Understanding molecular weight helps you accurately convert given masses to moles, a fundamental process for various chemical evaluations.

Unit Conversion

Unit conversion is a vital tool in chemistry, especially when dealing with different measurements of mass like milligrams, grams, kilograms, or micrograms. This allows for consistency when solving chemical equations or performing mole calculations.
The primary conversions you need to perform are:

• Milligrams to grams: 1 mg = 0.001 g
• Kilograms to grams: 1 kg = 1000 g
• Micrograms to grams: 1 µg = 0.000001 g

So, for an exercise involving oxycodone at 160.0 mg, you'd convert this to grams by multiplying by 0.001, resulting in 0.16 g.
Similarly, converting 2.82 kg of magnetite to grams involves multiplying by 1000, yielding 2820 g.
Understanding and executing these conversions correctly ensures that calculations align with the molar mass, which is always given in grams per mole, thus allowing accurate mole calculations.