Question

a teacher has given a lab student a white chemical sample and asks her to confirm that it contains 7.03×10²³ formula units of sodium hydroxide (naoh). using the balance in the laboratory, what mass of naoh would the student have to find to verify that her teacher was correct? round your answer to 3 significant figures. grams

Explanation:

Step1: Calculate the number of moles of NaOH

Use Avogadro's number \(N_A = 6.022\times10^{23}\text{ mol}^{-1}\). The formula for the number of moles \(n\) is \(n=\frac{N}{N_A}\), where \(N = 7.03\times 10^{23}\) formula units.

$$n=\frac{7.03\times 10^{23}}{6.022\times10^{23}\text{ mol}^{-1}}$$

$$n=\frac{7.03}{6.022}\text{ mol}\approx1.17\text{ mol}$$

Step2: Calculate the molar mass of NaOH

The molar mass of \(Na\) is \(M_{Na}=22.99\text{ g/mol}\), the molar mass of \(O\) is \(M_O = 16.00\text{ g/mol}\), and the molar mass of \(H\) is \(M_H=1.008\text{ g/mol}\). The molar mass of \(NaOH\), \(M = M_{Na}+M_O + M_H\)

$$M=(22.99 + 16.00+1.008)\text{ g/mol}=39.998\text{ g/mol}\approx40.0\text{ g/mol}$$

Step3: Calculate the mass of NaOH

Use the formula \(m=n\times M\). Substitute \(n = 1.17\text{ mol}\) and \(M = 40.0\text{ g/mol}\)

$$m=1.17\text{ mol}\times40.0\text{ g/mol}=46.8\text{ g}$$

Answer:

\(46.8\)