Question

Which of the following has the greater mass: \(0.72 \mathrm{~g}\) of \(\mathrm{O}_{2}\) or \(0.0011 \mathrm{~mol}\) of chlorophyll \(\left(\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{MgN}_{4} \mathrm{O}_{5}\right) ?\)

Short answer

Chlorophyll has a greater mass.

Step-by-step solution

Determine the Molar Mass of Oxygen

Oxygen gas \( \mathrm{O}_2 \) has two oxygen atoms. The atomic mass of one oxygen atom is approximately \( 16 \mathrm{~u} \). Thus, the molar mass of \( \mathrm{O}_2 \) is \( 2 \times 16 = 32 \mathrm{~g/mol} \).

Calculate Moles of Oxygen

To find the number of moles of \( \mathrm{O}_2 \), use the formula: \( n = \frac{m}{M} \), where \( n \) is moles, \( m \) is mass, and \( M \) is molar mass. Substitute the values: \( n = \frac{0.72}{32} = 0.0225 \mathrm{~mol} \).

Determine the Molar Mass of Chlorophyll

Calculate the molar mass of chlorophyll \( \mathrm{C}_{55} \mathrm{H}_{72} \mathrm{MgN}_{4} \mathrm{O}_{5} \). Using atomic masses: \( \mathrm{C} = 12 \mathrm{~u} \), \( \mathrm{H} = 1 \mathrm{~u} \), \( \mathrm{Mg} = 24 \mathrm{~u} \), \( \mathrm{N} = 14 \mathrm{~u} \), \( \mathrm{O} = 16 \mathrm{~u} \). Hence, \( \mathrm{C}_{55} \mathrm{H}_{72} \mathrm{MgN}_{4} \mathrm{O}_{5} = 55\times12 + 72\times1 + 24 + 4\times14 + 5\times16 = 893.5 \mathrm{~g/mol} \).

Calculate Mass of Chlorophyll

Use the formula \( m = n \times M \) to find the mass of chlorophyll, where \( n = 0.0011 \mathrm{~mol} \) and \( M = 893.5 \mathrm{~g/mol} \). Substitute the values: \( m = 0.0011 \times 893.5 = 0.98385 \mathrm{~g} \).

Compare Masses

We have \( 0.72 \mathrm{~g} \) of \( \mathrm{O}_2 \) and \( 0.98385 \mathrm{~g} \) of chlorophyll. Since \( 0.98385 \mathrm{~g} > 0.72 \mathrm{~g} \), the chlorophyll has a greater mass.

Key concepts

Molar Mass Calculation

When you calculate the molar mass, you're determining the mass of one mole of a substance. This is useful for converting between the mass of a substance and the number of moles.
To do so, sum up the atomic masses of all the atoms present in a molecule. For example:

• Oxygen (\( \mathrm{O}_2 \)) has a molar mass of \( 2 \times 16 = 32 \mathrm{~g/mol} \) because each oxygen atom weighs approximately 16 grams per mole.
• Chlorophyll (\( \mathrm{C}_{55} \mathrm{H}_{72} \mathrm{MgN}_{4} \mathrm{O}_{5} \)) has a molar mass of 893.5 grams per mole.

Accurate calculations are key. They help in predicting how substances react and what quantities are needed in chemical reactions.

Molecular Mass

Molecular mass refers to the sum of the atomic masses of all atoms in a given molecule. It is expressed in atomic mass units (u) and tells us how much one molecule of a substance weighs. For instance, chlorophyll's complex molecular structure involves multiple types of atoms:

• Carbon (C): 55 atoms each at 12 u
• Hydrogen (H): 72 atoms each at 1 u
• Magnesium (Mg): 1 atom at 24 u
• Nitrogen (N): 4 atoms each at 14 u
• Oxygen (O): 5 atoms each at 16 u

This adds to a total of 893.5 u for one chlorophyll molecule. Molecular mass helps us compare different molecules easily by running these straightforward calculations.

Stoichiometry

Stoichiometry is the part of chemistry that focuses on the quantitative relationships within chemical equations. It allows us to predict the amounts of products and reactants that will be involved in a chemical reaction.
By knowing the molar masses, we can convert between mass and moles to work with equations.For example:

• We used the formula \( n = \frac{m}{M} \) to find moles from a given mass.
• In the exercise, \( 0.72 \mathrm{~g} \) of oxygen is expressed as \( 0.0225 \mathrm{~mol} \).

This ability to switch between grams and moles provided us with the tools to compare the masses of different substances, such as oxygen gas and chlorophyll, effectively.

Chemical Formulas

Chemical formulas are symbolic representations of molecules that convey the types and numbers of atoms present. They provide a shorthand way of showing what makes up a compound. Examples include:

• \( \mathrm{O}_2 \), which signifies a diatomic molecule of oxygen with two oxygen atoms.
• \( \mathrm{C}_{55} \mathrm{H}_{72} \mathrm{MgN}_{4} \mathrm{O}_{5} \), which shows a compound with a complex composition consisting of multiple elements.

Understanding chemical formulas is foundational because they guide how we calculate molecular masses, understand reactivity, and perform stoichiometric calculations. Chemical formulas are like blueprints that help chemists and students alike comprehend the structures and potential reactions of molecules.