Question

what volume (ml) of 3.751 m hbr(aq) solution would contain 1.00×10²⁴ molecules of hbr?

Explanation:

Step1: Calculate the number of moles of HBr

Use Avogadro's number \(N = n\times N_A\), where \(N = 1.00\times10^{24}\) molecules, \(N_A=6.022\times 10^{23}\text{ mol}^{-1}\). Then \(n=\frac{N}{N_A}\).

$$n=\frac{1.00\times 10^{24}}{6.022\times 10^{23}\text{ mol}^{-1}}\approx1.66\text{ mol}$$

Step2: Calculate the volume of the solution

Use the formula \(M=\frac{n}{V}\) (where \(M = 3.751\text{ M}\), \(n = 1.66\text{ mol}\)), and solve for \(V\). Rearranging gives \(V=\frac{n}{M}\).

$$V=\frac{1.66\text{ mol}}{3.751\text{ mol/L}}\approx0.4426\text{ L}$$

Convert liters to milliliters: \(V = 0.4426\text{ L}\times1000\text{ mL/L}=443\text{ mL}\)

Answer:

\(443\text{ mL}\)