How many molecules are there in 4.0 moles of glucose? [Avogadro's number = 6.02 x  10$^{23}$]

Analysis

To find the number of molecules in a given number of moles, we use the relationship between the mole and Avogadro's constant. The mole is a standard unit in chemistry that represents a specific quantity of particles (atoms, molecules, or ions).

Concept

The relationship is defined by the formula: Number of molecules = Number of moles (n) × Avogadro's constant ($N_A$)

Where:

• n = 4.0 moles
• $N_A$ = $6.02 \times 10^{23}$ molecules/mol

Solution

1. Set up the calculation: Number of molecules = $4.0 \times (6.02 \times 10^{23})$

2. Multiply the coefficients: $4.0 \times 6.02 = 24.08$

3. Combine with the power of 10: $24.08 \times 10^{23}$

4. Convert to standard form (scientific notation): To express $24.08 \times 10^{23}$ in standard form, we move the decimal point one place to the left, which increases the exponent by 1: $2.408 \times 10^{24}$

Rounding to two decimal places (as seen in the options), we get $2.41 \times 10^{24}$.

Conclusion

Comparing our result to the given options, the correct value is $2.41 \times 10^{24}$. This matches option B.

Exam Tip

When dealing with Avogadro's constant, always watch your decimal placement. A common mistake is forgetting to adjust the exponent when converting from a number like $24.08$ to $2.41$. Remember: "Left adds, Right subtracts" (moving the decimal to the left adds to the exponent; moving it to the right subtracts from it).