Relative Formula Mass (Mr)
The Building Blocks: Atoms and Ions
To understand Relative Formula Mass, we must first start with the smallest building blocks: atoms. Every element has a characteristic mass called its Relative Atomic Mass (Ar). This number, found on the periodic table, tells us how heavy an atom of that element is compared to one-twelfth the mass of a carbon-12 atom. For instance, the Ar of hydrogen (H) is 1, oxygen (O) is 16, and sodium (Na) is 23.
Atoms can gain or lose electrons to form charged particles called ions. A positively charged ion is a cation (e.g., Na+), and a negatively charged ion is an anion (e.g., Cl-). These oppositely charged ions are strongly attracted to each other, forming ionic bonds and creating ionic compounds. The smallest unit of an ionic compound is a formula unit, which represents the simplest ratio of ions in the compound, like NaCl for sodium chloride (table salt).
Calculating Relative Formula Mass Step-by-Step
The Relative Formula Mass (Mr) of a compound is simply the sum of the Relative Atomic Masses of all the atoms shown in its chemical formula. The process is straightforward and can be broken down into a few key steps.
Step 1: Identify the Formula. Write down the chemical formula of the compound. For example, sodium chloride is NaCl.
Step 2: List the Elements and Count the Atoms. Identify each different element in the formula and count how many atoms of each are present.
- NaCl has 1 sodium (Na) atom and 1 chlorine (Cl) atom.
- Water, H2O, has 2 hydrogen (H) atoms and 1 oxygen (O) atom.
Step 3: Find the Relative Atomic Masses. Use the periodic table to find the Ar for each element.
- Ar of Na = 23
- Ar of Cl = 35.5
Step 4: Multiply and Add. For each element, multiply the number of atoms by its Ar. Then, add all these values together.
- For NaCl: Mr = (1 × 23) + (1 × 35.5) = 58.5
This means the formula unit of sodium chloride has a mass 58.5 times greater than one-twelfth of a carbon-12 atom.
Working with Compounds Containing Brackets
Some chemical formulas include brackets, which indicate a group of atoms that is repeated. A common example is calcium hydroxide, Ca(OH)2. The subscript "2" outside the bracket means that everything inside the bracket—the OH group—is taken twice.
Let's calculate the Mr for Ca(OH)2:
Step 1: Identify the atoms and their counts. The formula Ca(OH)2 contains:
- 1 Calcium (Ca) atom
- 2 Oxygen (O) atoms (from the two OH groups)
- 2 Hydrogen (H) atoms (from the two OH groups)
Step 2: Find the Ar values.
- Ar of Ca = 40
- Ar of O = 16
- Ar of H = 1
Step 3: Calculate the total mass.
Mr = (1 × 40) + (2 × 16) + (2 × 1)
Mr = 40 + 32 + 2 = 74
| Compound Name | Chemical Formula | Calculation | Relative Formula Mass (Mr) |
|---|---|---|---|
| Water | H2O | (2 × 1) + (1 × 16) | 18 |
| Carbon Dioxide | CO2 | (1 × 12) + (2 × 16) | 44 |
| Sulfuric Acid | H2SO4 | (2 × 1) + (1 × 32) + (4 × 16) | 98 |
| Calcium Carbonate | CaCO3 | (1 × 40) + (1 × 12) + (3 × 16) | 100 |
Applying Relative Formula Mass in Real-World Scenarios
Relative Formula Mass is not just a number to be calculated; it is a vital tool used in many practical chemical applications. One of the most important uses is in calculating the mass of a particular element within a given mass of a compound.
Example: Fertilizer Analysis
Ammonium nitrate, NH4NO3, is a common fertilizer because it is rich in nitrogen, an essential nutrient for plant growth. Farmers and chemists need to know how much nitrogen is in a bag of fertilizer. We can find this out using Mr.
First, calculate the Mr of ammonium nitrate:
Mr of NH4NO3 = (2 × Ar of N) + (4 × Ar of H) + (3 × Ar of O)
Mr = (2 × 14) + (4 × 1) + (3 × 16) = 28 + 4 + 48 = 80
Next, find the total mass of nitrogen in the formula. There are two nitrogen atoms, so total mass of N = 2 × 14 = 28.
The percentage of nitrogen by mass in ammonium nitrate is:
$(\frac{\text{Total mass of N in formula}}{\text{M}_r \text{ of compound}}) \times 100\%$
$(\frac{28}{80}) \times 100\% = 35\%$
This means that 35% of the mass of any sample of pure ammonium nitrate is nitrogen. This calculation helps in comparing the effectiveness of different fertilizers.
Common Mistakes and Important Questions
Q: I often confuse Mr with Ar. What is the main difference?
A: The key difference is what they refer to. Relative Atomic Mass (Ar) is the mass of a single atom of a specific element. Relative Formula Mass (Mr) is the mass of a whole formula unit of a compound, which is found by adding up the Ar values of all the atoms in that formula. Think of Ar as the weight of a single Lego brick, and Mr as the weight of the entire Lego model you built.
Q: Why do we sometimes use decimals in Ar values, like Chlorine being 35.5?
A: This is because many elements exist as a mixture of isotopes[3]. Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons, giving them different masses. Chlorine has two main isotopes: chlorine-35 and chlorine-37. The Ar value of 35.5 is an average that reflects the proportion of these isotopes found in a typical sample of chlorine. We use this weighted average in our Mr calculations.
Q: What is the most common calculation error when finding Mr?
A: The most frequent mistake is forgetting to multiply by the number of atoms, especially when the formula has subscripts or brackets. For example, in Mg(NO3)2, there are not 1 but 2 nitrogen atoms and 6 oxygen atoms (2 × 3). Always double-check that you have correctly counted all atoms, paying close attention to any subscripts outside of brackets.
Footnote
[1] Relative Atomic Mass (Ar): A dimensionless quantity representing the average mass of an atom of an element, measured on a scale where an atom of carbon-12 is exactly 12.
[2] Mole: The standard scientific unit (abbreviated 'mol') for measuring large amounts of very small entities such as atoms, molecules, or other specified particles. One mole contains exactly $6.02214076 \times 10^{23}$ elementary entities.
[3] Isotopes: Variants of a particular chemical element which differ in neutron number, and consequently in nucleon number. All isotopes of a given element have the same number of protons but different numbers of neutrons in each atom.