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Chapter 3: Problem 88

Perhaps the simplest way to calculate Avogadro's number is to compare the charge on the electron, first determined by Robert Millikan in 1909, with the charge on a mole of electrons, determined electrochemically (Chapter 18). These charges, in coulombs (C), are given in Appendix 1 . Use them to calculate Avogadro's number to five significant figures.

Short Answer

Expert verified
Answer: Avogadro's number is approximately 6.0221 x 10^23.

Step by step solution

01

Find the charge on an electron

According to the question, the charge on an electron (e) has been determined by Robert Millikan in 1909. Check Appendix 1 to find the value of the charge on an electron, which is approximately -1.602 \times 10^{-19} C.
02

Find the charge on a mole of electrons

The question also states that the charge on a mole of electrons has been determined electrochemically. Check Appendix 1 to find the value of the charge on a mole of electrons, which is approximately 96485 C.
03

Calculate Avogadro's number

Now that we have the charge on an electron (e) and the charge on a mole of electrons (Q), we can calculate Avogadro's number (N_A) using the formula: N_A = \frac{Q}{e} Substitute the values of Q and e into the equation: N_A = \frac{96485\:C}{-1.602 \times 10^{-19}\:C} Note that we do not need to consider the negative sign as both charges are negative and the result should be a posititve value. Calculating the result gives: N_A \approx 6.022 \times 10^{23} To five significant figures, the value of Avogadro's number is 6.0221 \times 10^{23}. So, the final result is:
04

Write down the final result

Avogadro's number, to five significant figures, is approximately 6.0221 \times 10^{23}.

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