The molar mass of carbon is 12 g/mol. How many moles are there in 3 grams of carbon?
The correct answer and explanation is :
Answer:
The number of moles (( n )) of a substance is calculated using the formula:
[
n = \frac{\text{mass}}{\text{molar mass}}
]
Given:
- Mass of carbon = 3 grams
- Molar mass of carbon = 12 g/mol
[
n = \frac{3 \text{ g}}{12 \text{ g/mol}}
]
[
n = 0.25 \text{ moles}
]
Thus, there are 0.25 moles of carbon in 3 grams of carbon.
Explanation:
Moles are a fundamental concept in chemistry that help relate the mass of a substance to the number of its constituent particles (atoms, molecules, or ions). The mole is defined as Avogadro’s number (6.022 × 10²³ particles) of any substance.
1. Understanding Molar Mass
The molar mass of an element is the mass of one mole of its atoms, expressed in grams per mole (g/mol). For carbon, the molar mass is 12 g/mol, meaning 1 mole of carbon atoms weighs 12 grams.
2. Using the Formula
To determine the number of moles in a given mass of a substance, we use the equation:
[
n = \frac{\text{mass of substance}}{\text{molar mass of substance}}
]
This equation shows that if we have a certain mass of a substance and know its molar mass, we can find how many moles it contains.
3. Substituting the Given Values
In this case, the mass of carbon provided is 3 grams. Since the molar mass of carbon is 12 g/mol, we divide:
[
3 \text{ g} \div 12 \text{ g/mol} = 0.25 \text{ moles}
]
4. What This Means
This result tells us that 3 grams of carbon contain 0.25 moles of carbon atoms, which means there are:
[
0.25 \times 6.022 \times 10^{23} = 1.5055 \times 10^{23} \text{ carbon atoms}
]
Thus, even a small amount of carbon contains an enormous number of atoms!