What is the atomic mass of copper, Cu? 2. How many grams are there in 36.34 moles of Cu? 3. How many moles are there in 3.7 × 105 grams of Cu? 4. How many copper atoms are there in 92.56 moles of Cu? 5. How many copper atoms are there in 0.104 grams of Cu
The Correct Answer and Explanation is:
Answers:
- Atomic mass of copper (Cu):
63.55 g/mol - Mass in grams for 36.34 moles of Cu:
Mass=Moles×Atomic Mass\text{Mass} = \text{Moles} \times \text{Atomic Mass}
=36.34 mol×63.55 g/mol=2,311.65 g= 36.34 \, \text{mol} \times 63.55 \, \text{g/mol} = \boxed{2,311.65 \, \text{g}} - Moles in 3.7 × 10⁵ grams of Cu:
Moles=MassAtomic Mass\text{Moles} = \frac{\text{Mass}}{\text{Atomic Mass}}
=3.7×10563.55≈5,823.86 mol= \frac{3.7 \times 10^5}{63.55} \approx \boxed{5,823.86 \, \text{mol}} - Atoms in 92.56 moles of Cu:
Atoms=Moles×Avogadro’s Number\text{Atoms} = \text{Moles} \times \text{Avogadro’s Number}
=92.56×6.022×1023≈5.574×1025 atoms= 92.56 \times 6.022 \times 10^{23} \approx \boxed{5.574 \times 10^{25} \, \text{atoms}} - Atoms in 0.104 grams of Cu:
Step 1: Find moles
Moles=0.10463.55≈0.001637 mol\text{Moles} = \frac{0.104}{63.55} \approx 0.001637 \, \text{mol}
Step 2: Multiply by Avogadro’s Number
Atoms=0.001637×6.022×1023≈9.86×1020 atoms\text{Atoms} = 0.001637 \times 6.022 \times 10^{23} \approx \boxed{9.86 \times 10^{20} \, \text{atoms}}
Explanation
Copper (Cu) is a metallic element with an atomic mass of 63.55 grams per mole, which means that one mole of copper atoms weighs 63.55 grams. In chemistry, the mole is a fundamental unit that measures the amount of substance. One mole always contains Avogadro’s number of particles, which is approximately 6.022 × 10²³ atoms/molecules.
To determine how many grams are in a given number of moles (like in question 2), we multiply the number of moles by copper’s atomic mass. This gives us the total mass in grams. Similarly, if we know the mass in grams (question 3), we divide by the atomic mass to find the number of moles.
When dealing with atoms (questions 4 and 5), we need to connect moles to atoms. Since each mole contains Avogadro’s number of atoms, multiplying the number of moles by 6.022×10236.022 \times 10^{23} gives the total number of atoms.
In question 5, since we start with grams, we first convert to moles and then to atoms, using the same process in two steps. This method allows us to calculate the atomic-level quantity from a macroscopic mass.
Understanding these conversions is vital in chemistry, especially when working with chemical reactions and compositions. It bridges the gap between the microscopic world of atoms and the macroscopic quantities we measure in laboratories. Copper, as a common element used in wiring and coins, provides a practical example to apply these calculations.
