Question

What mass of aluminum has a total nuclear charge of 1.0 C? Aluminum has atomic number 13

Short answer

The mass of aluminum is$m=2.15\times {10}^{-5}g$

Step-by-step solution

Content Introduction

Aluminum is a chemical element with the atomic number 13 and the symbol Al. Aluminum is a solid at ambient temperature and is classified as a post-transition metal.

Content Explanation

The charge is represented by $Q$and for an object its charge equals the number of carriers N times the charge of carrier which is $-e$for electrons and $+e$for protons.

Therefore, $Q=Ne$

$e=-1.6\times {10}^{-19}C$,$Q=1C$

Put the values in the equation$Q=Ne$

$$\begin{gathered} Q=Ne \\ N=\frac{Q}{e} \\ N=\frac{1C}{1.6\times {10}^{-19}C} \\ N=6.25\times {10}^{18}protons \end{gathered}$$

Conclusion

The number of moles is calculated by dividing the mass of the object (m) with its molecular weight (M). We are given here$1moleculeofaluminium=13protons$

According to Avogadro's number

The number of moles is

$$\begin{gathered} n=\frac{N}{13N_A} \\ n=\frac{6.25\times {10}^{18}protons}{13(6.02\times {10}^{23}molecules)} \\ n=7.98\times {10}^{-7}moles \end{gathered}$$

The molecular weight of aluminum is $27g/mole$

The mass is

$$\begin{gathered} m=nM \\ m=(7.98\times {10}^{-7}moles)(27g/mol) \\ m=2.15\times {10}^{-5}g \end{gathered}$$