Acetaminophen, a pain reliever and a fever reducer, has the formula C8H9O2N. What is the mass in grams of 0.30 mole sample of this pain reliever? with solution
The correct answer and explanation is:
To calculate the mass of a sample, we can use the formula: mass=moles×molar mass\text{mass} = \text{moles} \times \text{molar mass}
Step 1: Find the molar mass of acetaminophen (C₈H₉O₂N)
To do this, we need to add the atomic masses of all the elements present in acetaminophen.
- Carbon (C) has an atomic mass of approximately 12.01 g/mol.
- Hydrogen (H) has an atomic mass of approximately 1.008 g/mol.
- Oxygen (O) has an atomic mass of approximately 16.00 g/mol.
- Nitrogen (N) has an atomic mass of approximately 14.01 g/mol.
Now, let’s calculate the molar mass of C₈H₉O₂N. Molar mass of acetaminophen=(8×12.01 g/mol)+(9×1.008 g/mol)+(2×16.00 g/mol)+(1×14.01 g/mol)\text{Molar mass of acetaminophen} = (8 \times 12.01 \, \text{g/mol}) + (9 \times 1.008 \, \text{g/mol}) + (2 \times 16.00 \, \text{g/mol}) + (1 \times 14.01 \, \text{g/mol}) =96.08 g/mol+9.072 g/mol+32.00 g/mol+14.01 g/mol= 96.08 \, \text{g/mol} + 9.072 \, \text{g/mol} + 32.00 \, \text{g/mol} + 14.01 \, \text{g/mol} =151.162 g/mol= 151.162 \, \text{g/mol}
Thus, the molar mass of acetaminophen is 151.162 g/mol.
Step 2: Calculate the mass of 0.30 mole of acetaminophen
Now, we can use the formula for mass: mass=moles×molar mass\text{mass} = \text{moles} \times \text{molar mass}
Given that we have 0.30 moles of acetaminophen, the mass is: mass=0.30 moles×151.162 g/mol\text{mass} = 0.30 \, \text{moles} \times 151.162 \, \text{g/mol} mass=45.3486 g\text{mass} = 45.3486 \, \text{g}
Therefore, the mass of a 0.30 mole sample of acetaminophen is 45.35 grams.
Explanation
The molar mass of a compound is simply the sum of the atomic masses of all atoms in the molecule. Once we know the molar mass, we can use the relationship between moles and mass to find the desired quantity. This method is used frequently in chemistry to convert between the amount of substance (in moles) and its mass (in grams).