Answer :
To determine the mass in grams of \( 4.25 \times 10^3 \) moles of \( \text{N}_2 \) (Nitrogen gas), we need to use the molar mass of \( \text{N}_2 \), which is \( 28.02 \) grams per mole.
Step-by-step solution:
1. Identify the given values:
- Moles of \( \text{N}_2 \): \( 4.25 \times 10^3 \text{ mol} \)
- Molar mass of \( \text{N}_2 \): \( 28.02 \text{ g/mol} \)
2. Use the formula to calculate the mass:
[tex]\[ \text{Mass} = \text{moles} \times \text{molar mass} \][/tex]
3. Substitute the given values into the formula:
[tex]\[ \text{Mass} = 4.25 \times 10^3 \text{ mol} \times 28.02 \text{ g/mol} \][/tex]
4. Perform the multiplication:
[tex]\[ \text{Mass} = 4.25 \times 10^3 \times 28.02 \][/tex]
5. Calculate the product:
- First, multiply \( 4.25 \times 10^3 \) which is \( 4250 \).
- Then multiply \( 4250 \) by \( 28.02 \).
[tex]\[ 4250 \times 28.02 = 119085 \][/tex]
6. Write the result with correct units:
[tex]\[ \text{Mass of } 4.25 \times 10^3 \text{ mol of } \text{N}_2 = 119085 \text{ grams} \][/tex]
Now, comparing this to the given multiple-choice options:
A) \(2.35 \times 10^{-4} g\)
B) \(1.52 \times 10^2 g\)
C) \(5.95 \times 10^4 g\)
D) \(1.19 \times 10^5 g\)
The correct answer is:
[tex]\[ \boxed{1.19 \times 10^5 \text{ grams}} \][/tex]
Step-by-step solution:
1. Identify the given values:
- Moles of \( \text{N}_2 \): \( 4.25 \times 10^3 \text{ mol} \)
- Molar mass of \( \text{N}_2 \): \( 28.02 \text{ g/mol} \)
2. Use the formula to calculate the mass:
[tex]\[ \text{Mass} = \text{moles} \times \text{molar mass} \][/tex]
3. Substitute the given values into the formula:
[tex]\[ \text{Mass} = 4.25 \times 10^3 \text{ mol} \times 28.02 \text{ g/mol} \][/tex]
4. Perform the multiplication:
[tex]\[ \text{Mass} = 4.25 \times 10^3 \times 28.02 \][/tex]
5. Calculate the product:
- First, multiply \( 4.25 \times 10^3 \) which is \( 4250 \).
- Then multiply \( 4250 \) by \( 28.02 \).
[tex]\[ 4250 \times 28.02 = 119085 \][/tex]
6. Write the result with correct units:
[tex]\[ \text{Mass of } 4.25 \times 10^3 \text{ mol of } \text{N}_2 = 119085 \text{ grams} \][/tex]
Now, comparing this to the given multiple-choice options:
A) \(2.35 \times 10^{-4} g\)
B) \(1.52 \times 10^2 g\)
C) \(5.95 \times 10^4 g\)
D) \(1.19 \times 10^5 g\)
The correct answer is:
[tex]\[ \boxed{1.19 \times 10^5 \text{ grams}} \][/tex]
