Question

how many grams of n₂ are needed to make 444 g of nbr₃? (answer = 24.5 g)
n₂ + 3 br₂ → 2 nbr₃ + 44.0 kj
the molar mass of nbr₃ is 253.719 g and the molar mass of n₂ is 28.013 g
1 mol nbr₃
(444 g nbr₃)(------------------) = 1 mol nbr₃
2 g nbr₃
3 mol n₂
4 mol nbr₃ (----------------) = 5 mol n₂
6 mol nbr₃
7 g n₂
8 mol n₂ (----------------) = 9 g n₂
10 mol n₂
a. 1 b. 2 c. 3 d. 4 e. 5 f. 253.719 g. 3.38×10⁰
h. 3.26×10³ i. 44.0 j. 1.33×10⁻² k. 9.77×10³ l. 4.44×10²
m. 6.66×10² n. 500.0 o. 556 p. 90.0 q. 3.2852 r. 159.81

Explanation:

Step1: Calculate moles of \(NBr_3\)

Using the formula \(n=\frac{m}{M}\), where \(m = 444\space g\) (mass of \(NBr_3\)) and \(M=253.719\space g/mol\) (molar mass of \(NBr_3\)).
\((444\space g\space NBr_3)\times(\frac{1\space mol\space NBr_3}{253.719\space g\space NBr_3})\)
\(n_{NBr_3}=\frac{444}{253.719}\approx1.75\space mol\)

Step2: Use mole ratio from the balanced equation

The balanced equation is \(N_2 + 3Br_2
ightarrow2NBr_3+44.0\space kJ\). The mole ratio of \(N_2\) to \(NBr_3\) is \(1:2\).
\(1.75\space mol\space NBr_3\times(\frac{1\space mol\space N_2}{2\space mol\space NBr_3})\)
\(n_{N_2}=\frac{1.75}{2}= 0.875\space mol\)

Step3: Calculate mass of \(N_2\)

Using the formula \(m = n\times M\), where \(n = 0.875\space mol\) (moles of \(N_2\)) and \(M = 28.013\space g/mol\) (molar mass of \(N_2\)).
\(0.875\space mol\space N_2\times(\frac{28.013\space g\space N_2}{1\space mol\space N_2})\)
\(m_{N_2}=0.875\times28.013 = 24.5\space g\)

Now for filling the blanks:

• For \((444\space g\space NBr_3)(\frac{1\space mol\space NBr_3}{253.719\space g\space NBr_3})\), blank \(1\) is \(1.75\approx1.75\times10^{0}\), blank \(2\) is \(253.719\) (F)
• For \(1.75\space mol\space NBr_3(\frac{1\space mol\space N_2}{2\space mol\space NBr_3})\), blank \(3\) is \(1\) (C), blank \(4\) is \(1.75\approx1.75\times 10^{0}\), blank \(5\) is \(0.875\approx8.75\times10^{-1}\), blank \(6\) is \(2\) (B)
• For \(0.875\space mol\space N_2(\frac{28.013\space g\space N_2}{1\space mol\space N_2})\), blank \(7\) is \(28.013\) (S), blank \(8\) is \(0.875\approx8.75\times10^{-1}\), blank \(9\) is \(24.5\approx2.45\times10^{1}\), blank \(10\) is \(1\) (A)

Answer:

1. \(1.75\times 10^{0}\)
2. F. \(253.719\)
3. C. \(3\)
4. \(1.75\times 10^{0}\)
5. \(8.75\times 10^{-1}\)
6. B. \(2\)
7. S. \(28.013\)
8. \(8.75\times 10^{-1}\)
9. \(2.45\times 10^{1}\)
10. A. \(1\)