Question

Find the mass in kilograms of${\mathbf{\text{7.5×10}}}^{\mathbf{\text{24}}}$atoms of arsenic, which has a molar mass of$\mathbf{\text{74.9}}\frac{\mathbf{\text{g}}}{\mathbf{\text{mol}}}\mathbf{\text{.}}$

Short answer

The mass in kilograms of $7.5\times {10}^{24}$atoms of arsenicis 0.933 kg.

Step-by-step solution

Stating thegiven data

1. Total number of atoms of arsenic,$N=7.50\times {10}^{24}$
2. Molar mass,$\begin{array}{c}M=74.9\frac{\text{g}}{\text{mol}}\\ =74.9\times {10}^{-3}\frac{\text{kg}}{\text{mol}}\end{array}$
3. Avogadro’sNumber,$N_A=6.02\times {10}^{23}\text{permol}$.

Determiningthe concept

By using Equation 19-4 for the mass of each atom, we calculate the total mass of the arsenic atom in kilograms. A mole is related to mass by the equation${\mathbf{mN}}_A$.

The formula is as follows:

$M=m{N}_A$

Here, m isthe mass of each atom, M is the molar mass and$N_A$ is Avogadro’snumber

Determining the mass in kilograms of  7.5 ×1024atoms of arsenic

According to Equation19-4, M is molar mass and $N_A$is the Avogadro’snumber (constant).

$M=m{N}_A$

where m is the mass of each atom. By rearranging the given equation, we have

$m=\frac{M}{N_A}$

For N atoms

$m=\frac{NM}{N_A}$

By substituting the given value, the total mass is

$m=\frac{7.50\times {10}^{24}\times 74.9\times {10}^{-3}}{6.02\times {10}^{23}}$

$m=0.933\text{\hspace{0.17em}kg}$

Hence, the mass in kilograms of $7.5\times {10}^{24}$atoms of arsenicis 0.933 kg.