/*! 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 29 Find the mass (in \(\mathrm{kg}\... [FREE SOLUTION] | 91影视

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Chapter 13: Problem 29

Find the mass (in \(\mathrm{kg}\) ) of one molecule of \(\mathrm{CO}_{2}\)

Short Answer

Expert verified
Answer: The mass of one CO2 molecule is approximately \(7.310 \times 10^{-26} kg\).

Step by step solution

01

Find the molar mass of CO2

To find the molar mass of CO2, we need to know the molar mass of each element and their respective number of atoms in a CO2 molecule. A CO2 molecule is composed of one carbon (C) atom and two oxygen (O) atoms. The molar mass of carbon is 12.01 g/mol, and the molar mass of oxygen is 16.00 g/mol. To find the molar mass of CO2, multiply the molar mass of each element by the number of its atoms in the molecule and then add the results: Molar mass of CO2 = (1 脳 12.01 g/mol) + (2 脳 16.00 g/mol) = 12.01 g/mol + 32.00 g/mol = 44.01 g/mol.
02

Convert g/mol to kg/mol

Since we need to find the mass in kg, we first need to convert the molar mass from grams to kilograms. We know that 1 kg = 1000 g, so divide the molar mass by 1000: Molar mass of CO2 = 44.01 g/mol 梅 1000 = 0.04401 kg/mol.
03

Use Avogadro's number to find the mass of one molecule

Now, we'll use Avogadro's number (6.022 脳 10^{23} ) to find the mass of a single CO2 molecule. Since there are 6.022 脳 10^{23} molecules in a mole, we can divide the molar mass by Avogadro's number to find the mass of one molecule: Mass of one CO2 molecule = \(\frac{0.04401 kg/mol}{6.022 \times 10^{23} molecules/mol}\).
04

Calculate the mass of one molecule

Now, you can perform the operation to find the mass of a single CO2 molecule: Mass of one CO2 molecule = \(\frac{0.04401 kg/mol}{6.022 \times 10^{23} molecules/mol} \approx 7.310 \times 10^{-26} kg\). So, the mass of one CO2 molecule is approximately \(7.310 \times 10^{-26} kg\).

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Most popular questions from this chapter

How many hydrogen atoms are present in \(684.6 \mathrm{g}\) of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right) ?\)
Agnes Pockels \((1862-1935)\) was able to determine Avogadro's number using only a few household chemicals, in particular oleic acid, whose formula is \(\mathrm{C}_{18} \mathrm{H}_{34} \mathrm{O}_{2}\) (a) What is the molar mass of this acid? (b) The mass of one drop of oleic acid is \(2.3 \times 10^{-5} \mathrm{g}\) and the volume is $2.6 \times 10^{-5} \mathrm{cm}^{3} .$ How many moles of oleic acid are there in one drop? (c) Now all Pockels needed was to find the number of molecules of oleic acid. Luckily, when oleic acid is spread out on water, it lines up in a layer one molecule thick. If the base of the molecule of oleic acid is a square of side \(d\), the height of the molecule is known to be \(7 d .\) Pockels spread out one drop of oleic acid on some water, and measured the area to be \(70.0 \mathrm{cm}^{2}\) Using the volume and the area of oleic acid, what is \(d ?\) (d) If we assume that this film is one molecule thick, how many molecules of oleic acid are there in the drop? (e) What value does this give you for Avogadro's number?
A temperature change \(\Delta T\) causes a volume change \(\Delta V\) but has no effect on the mass of an object. (a) Show that the change in density $\Delta \rho\( is given by \)\Delta \rho=-\beta \rho \Delta T$. (b) Find the fractional change in density \((\Delta \rho / \rho)\) of a brass sphere when the temperature changes from \(32^{\circ} \mathrm{C}\) to \(-10.0^{\circ} \mathrm{C}\)
Steel railroad tracks of length \(18.30 \mathrm{m}\) are laid at $10.0^{\circ} \mathrm{C} .$ How much space should be left between the track sections if they are to just touch when the temperature is \(50.0^{\circ} \mathrm{C} ?\)
In intergalactic space, there is an average of about one hydrogen atom per \(\mathrm{cm}^{3}\) and the temperature is \(3 \mathrm{K}\) What is the absolute pressure?
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