Question

calculate the mass of tetraborane (b₄h₁₀) that contains a trillion (1.00×10¹²) hydrogen atoms. be sure your answer has a unit symbol if necessary, and round it to 3 significant digits.

Explanation:

Step1: Determine moles of hydrogen atoms

Use Avogadro's number ($N_A = 6.022\times 10^{23}\text{ atoms/mol}$). The number of moles of hydrogen atoms ($n_H$) is calculated by $n_H=\frac{N}{N_A}$, where $N = 1.00\times 10^{12}$ atoms. So $n_H=\frac{1.00\times 10^{12}\text{ atoms}}{6.022\times 10^{23}\text{ atoms/mol}}=1.66\times 10^{-12}\text{ mol}$.

Step2: Relate moles of hydrogen to moles of $B_4H_{10}$

In one molecule of $B_4H_{10}$, there are 10 hydrogen atoms. So the number of moles of $B_4H_{10}$ ($n_{B_4H_{10}}$) is $n_{B_4H_{10}}=\frac{n_H}{10}$. Substituting the value of $n_H$, we get $n_{B_4H_{10}}=\frac{1.66\times 10^{-12}\text{ mol}}{10}=1.66\times 10^{-13}\text{ mol}$.

Step3: Calculate the molar - mass of $B_4H_{10}$

The molar - mass of $B$ is approximately $M_B = 10.81\text{ g/mol}$ and the molar - mass of $H$ is approximately $M_H = 1.01\text{ g/mol}$. The molar - mass of $B_4H_{10}$ ($M_{B_4H_{10}}$) is $M_{B_4H_{10}}=4\times10.81\text{ g/mol}+10\times1.01\text{ g/mol}=43.24\text{ g/mol}+10.1\text{ g/mol}=53.34\text{ g/mol}$.

Step4: Calculate the mass of $B_4H_{10}$

Use the formula $m = n\times M$. Substituting $n = n_{B_4H_{10}}$ and $M = M_{B_4H_{10}}$, we get $m=(1.66\times 10^{-13}\text{ mol})\times53.34\text{ g/mol}=8.85\times 10^{-12}\text{ g}$.

Answer:

$8.85\times 10^{-12}\text{ g}$