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Chapter 8: Problem 106

If an average sodium atom weighs 22.99 amu, how many sodium atoms are contained in \(1.98 \times 10^{13}\) amu of sodium? What will \(3.01 \times 10^{23}\) sodium atoms weigh?

Short Answer

Expert verified
In conclusion, 1.98 脳 10^13 amu of sodium contains around \(8.61 \times 10^{11}\) sodium atoms, and the mass of \(3.01 \times 10^{23}\) sodium atoms is approximately \(6.92 \times 10^{24}\) amu.

Step by step solution

01

Finding the number of sodium atoms

Given weight of sodium = 1.98 x 10^13 amu Average weight of single sodium atom = 22.99 amu To find the number of sodium atoms in the given mass, we will divide the total mass by the average mass of a single sodium atom: Number of sodium atoms = (Given weight of sodium) / (Average weight of single sodium atom)
02

Calculating the number of sodium atoms

We can now plug in the given values and calculate the number of sodium atoms: Number of sodium atoms = \(\frac{1.98 \times 10^{13}\, \text{amu}}{22.99\, \text{amu}}\) Number of sodium atoms 鈮� 8.61 脳 10^11 So there are approximately 8.61 脳 10^11 sodium atoms in 1.98 脳 10^13 amu of sodium.
03

Calculating the mass of given number of sodium atoms

Now, we have to find the mass of 3.01 脳 10^23 sodium atoms. We can use the following formula to calculate it: Mass of sodium atoms = (Number of sodium atoms) 脳 (Average weight of single sodium atom)
04

Plugging in the values of the known parameters

We can now plug in the given values and calculate the mass of 3.01 脳 10^23 sodium atoms: Mass of sodium atoms = \(3.01 \times 10^{23}\ \text{sodium atoms} \times 22.99\ \text{amu}\) Mass of sodium atoms 鈮� 6.92 脳 10^24 amu So the mass of 3.01 脳 10^23 sodium atoms is approximately 6.92 脳 10^24 amu. In conclusion, 1.98 脳 10^13 amu of sodium contains around 8.61 脳 10^11 sodium atoms, and the mass of 3.01 脳 10^23 sodium atoms is approximately 6.92 脳 10^24 amu.

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