Question

1. how many moles are in $3.01 \times 10^{23}$ particles of aluminum (al)?

a. 0.25 mol
b. 0.50 mol
c. 1.00 mol
d. 2.00 mol

1. a sample contains 33.6 l of gas at stp. how many moles are present?

a. 0.50 mol
b. 1.00 mol
c. 1.50 mol
d. 2.00 mol

Explanation:

Step1: Use Avogadro's number formula

Moles = $\frac{\text{Number of particles}}{\text{Avogadro's number}}$, where Avogadro's number = $6.02 \times 10^{23}$ particles/mol
Expression: $\text{Moles of Al} = \frac{3.01 \times 10^{23}}{6.02 \times 10^{23}}$

Step2: Calculate moles of Al

Simplify the expression
Expression: $\text{Moles of Al} = 0.50$ mol
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Step1: Use STP gas volume conversion

At STP, 1 mol of gas = 22.4 L
Expression: $\text{Moles of gas} = \frac{\text{Volume of gas}}{22.4\ \text{L/mol}}$

Step2: Calculate moles of gas

Substitute the given volume
Expression: $\text{Moles of gas} = \frac{33.6}{22.4} = 1.50$ mol

Answer:

1. B. 0.50 mol
2. C. 1.50 mol