/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 30 The mass of \(1 \mathrm{mol}\) o... [FREE SOLUTION] | 91影视

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Chapter 13: Problem 30

The mass of \(1 \mathrm{mol}\) of \(^{13} \mathrm{C}\) (carbon- 13 ) is $13.003 \mathrm{g}$. (a) What is the mass in \(u\) of one \(^{13} \mathrm{C}\) atom? (b) What is the mass in kilograms of one \(^{13} \mathrm{C}\) atom?

Short Answer

Expert verified
Answer: The mass of one \(^{13} \mathrm{C}\) atom is \(13.003 \ \text{u}\) in atomic mass units and \(2.1611 \times 10^{-26} \ \text{kg}\) in kilograms.

Step by step solution

01

(Find the mass in atomic mass units)

Using the given mass of 1 mol of \(^{13} \mathrm{C}\) atoms which is \(13.003 \mathrm{g}\), we will first find the mass of one \(^{13} \mathrm{C}\) atom in atomic mass units (u). Since there are Avogadro's number (\(6.022 \times 10^{23}\) atoms) in 1 mol, we can find the mass of one \(^{13} \mathrm{C}\) atom in atomic mass units by dividing the molar mass by Avogadro's number: $$ \text{Mass in u} = \frac{13.003 \mathrm{g/mol}}{6.022 \times 10^{23} \text{atoms/mol}} $$
02

(Calculate the mass in atomic mass units)

Now we will plug in the numbers and multiply to get our result: $$ \text{Mass in u} = \frac{13.003 \text{g/mol}}{6.022 \times 10^{23} \text{atoms/mol}} \times \frac{1 \ \text{mol}}{6.022 \times 10^{23} \ \text{atoms}} = 13.003 \ \text{u} $$ So the mass of one \(^{13} \mathrm{C}\) atom in atomic mass units is \(13.003 \ \text{u}\).
03

(Find the mass in kilograms)

Next, we will find the mass of one \(^{13} \mathrm{C}\) atom in kilograms. To do this, we will use the conversion factor between grams and atomic mass units, which is: $$ 1 \ \text{u} = 1.6605 \times 10^{-27} \ \text{kg} $$ We can multiply the mass in atomic mass units by this conversion factor to find the mass in kilograms: $$ \text{Mass in kg} = 13.003 \ \text{u} \times \frac{1.6605 \times 10^{-27} \ \text{kg}}{1 \ \text{u}} $$
04

(Calculate the mass in kilograms)

Now we will plug in the numbers and multiply to get our result: $$ \text{Mass in kg} = 13.003 \ \text{u} \times \frac{1.6605 \times 10^{-27} \ \text{kg}}{1 \ \text{u}} = 2.1611 \times 10^{-26} \ \text{kg} $$ So the mass of one \(^{13} \mathrm{C}\) atom in kilograms is \(2.1611 \times 10^{-26} \ \text{kg}\). In conclusion, the mass of one \(^{13} \mathrm{C}\) atom is \(13.003 \ \text{u}\) in atomic mass units and \(2.1611 \times 10^{-26} \ \text{kg}\) in kilograms.

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