Question

question 24 (10 points)
how many moles of fructose are in a sample containing 1.43 × 10²⁴ molecules of fructose?
2.37 mol
8.61 × 10⁴⁷ mol
0.420 mol
1.16 × 10⁻⁴⁸ mol
2.38 × 10⁻¹ mol

Explanation:

Step1: Use Avogadro's number

Avogadro's number \(N_A = 6.022\times 10^{23}\text{ molecules/mol}\). The formula to find the number of moles \(n\) is \(n=\frac{N}{N_A}\), where \(N\) is the number of molecules.
Given \(N = 1.43\times 10^{24}\text{ molecules}\).

Step2: Calculate the number of moles

Substitute the values into the formula: \(n=\frac{1.43\times 10^{24}}{6.022\times 10^{23}}\).
Using the rule of exponents \(\frac{a^m}{a^n}=a^{m - n}\) and \(\frac{1.43}{6.022}\approx0.237\), \(a = 10\), \(m = 24\), \(n=23\). So \(n=\frac{1.43}{6.022}\times10^{24 - 23}\approx0.237\times10^{1}=2.37\text{ mol}\)

Answer:

\(2.37\text{ mol}\)