In the gaseous state chlorine exists as a diatomic molecule Cl2 (molar mass=70.9g/mol). Calculate the number of moles present in 120 g of chlorine gas.
Express the quantity and moles to three significant figures.
The correct answer and explanation is :
To calculate the number of moles of chlorine gas (Cl₂) in 120 grams, use the following formula:
[
\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}
]
Step-by-step Calculation:
Given:
- Mass of chlorine gas = 120 g
- Molar mass of chlorine gas (Cl₂) = 70.9 g/mol
[
\text{Moles} = \frac{120\ \text{g}}{70.9\ \text{g/mol}} \approx 1.692\ \text{mol}
]
Answer:
[
\boxed{1.69\ \text{mol}}
]
Explanation (300+ words):
The concept of mole is fundamental in chemistry and allows chemists to count particles (atoms, molecules, ions) by weighing them. One mole of any substance contains Avogadro’s number of particles, which is approximately ( 6.022 \times 10^{23} ) entities.
In this problem, we are given chlorine gas, which naturally exists as diatomic molecules (Cl₂), not individual chlorine atoms. This is important because it affects the molar mass used in the calculation. While the atomic mass of a single chlorine atom is about 35.45 g/mol, the molar mass of Cl₂ is:
[
35.45 \times 2 = 70.9\ \text{g/mol}
]
This value represents the mass of one mole of Cl₂ molecules.
To determine how many moles are in 120 grams of chlorine gas, we divide the total mass by the molar mass. The formula used is:
[
\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}
]
Substituting the values:
[
\frac{120}{70.9} \approx 1.692\ \text{mol}
]
Since the question specifies to express the answer to three significant figures, we round 1.692 to 1.69 mol.
This value tells us that 120 grams of chlorine gas contains approximately 1.69 moles, or equivalently, about ( 1.69 \times 6.022 \times 10^{23} \approx 1.02 \times 10^{24} ) chlorine molecules.
Understanding molar conversions like this is essential in stoichiometry, allowing scientists to relate mass to number of particles in chemical reactions, gas laws, and concentration calculations.