/*! 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 35 Calculate the following quantiti... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 35

Calculate the following quantities: (a) mass, in grams, of 0.105 mol sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) (b) moles of \(\mathrm{Zn}\left(\mathrm{NO}_{3}\right)_{2}\) in \(143.50 \mathrm{~g}\) of this substance (c) number of molecules in \(1.0 \times 10^{-6} \mathrm{~mol} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) (d) number of \(\mathrm{N}\) atoms in \(0.410 \mathrm{~mol} \mathrm{NH}_{3}\)

Short Answer

Expert verified
(a) 35.94 g sucrose; (b) 0.757 mol Zn(NO3)2; (c) 6.022 脳 10^17 molecules of C2H5OH; (d) 2.47 脳 10^23 N atoms in NH3.

Step by step solution

01

Calculate Molar Mass (a)

Identify the molar mass of sucrose \ \( \text{C}_{12}\text{H}_{22}\text{O}_{11} \). Calculate by adding the atomic masses of 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms: - Carbon: \(12 \times 12.01 = 144.12\) g/mol- Hydrogen: \(22 \times 1.008 = 22.176\) g/mol- Oxygen: \(11 \times 16.00 = 176.00\) g/molAdd them together: \[ \text{Molar mass of sucrose} = 342.30 \text{ g/mol} \]
02

Mass of Sucrose (a)

To find the mass in grams of 0.105 mol sucrose, use the formula:\[ \text{Mass} = \text{moles} \times \text{molar mass} \]\[ \text{Mass} = 0.105 \text{ mol} \times 342.30 \text{ g/mol} = 35.94 \text{ g} \]
03

Calculate Molar Mass of Zn(NO3)2 (b)

Identify the molar mass of \( \text{Zn(NO}_3)_2 \):- Zinc: \(1 \times 65.38 = 65.38\) g/mol- Nitrogen: \(2 \times 14.01 = 28.02\) g/mol- Oxygen: \(6 \times 16.00 = 96.00\) g/molAdd them together:\[ \text{Molar mass of } \text{Zn(NO}_3)_2 = 189.40 \text{ g/mol} \]
04

Moles of Zn(NO3)2 (b)

To find the moles of \( \text{Zn(NO}_3)_2 \) in 143.50 g, use the formula:\[ \text{Moles} = \frac{\text{Mass}}{\text{Molar mass}} \]\[ \text{Moles} = \frac{143.50 \text{ g}}{189.40 \text{ g/mol}} \approx 0.757 \text{ mol} \]
05

Calculate Molecules of C2H5OH (c)

Start with \(1.0 \times 10^{-6} \text{ mol} \) of \( \text{C}_2\text{H}_5\text{OH} \). Use Avogadro's number, \(6.022 \times 10^{23} \text{ molecules/mol} \):\[ \text{number of molecules} = \text{moles} \times \text{Avogadro's number} \]\[ \text{number of molecules} = 1.0 \times 10^{-6} \times 6.022 \times 10^{23} \]\[ \text{number of molecules} \approx 6.022 \times 10^{17} \]
06

Calculate Nitrogen Atoms in NH3 (d)

Start with \(0.410 \text{ mol} \text{ NH}_3\). Each molecule contains 1 nitrogen atom. Use Avogadro's number to find the total:\[ \text{number of N atoms} = \text{moles} \times \text{Avogadro's number} \]\[ \text{number of N atoms} = 0.410 \times 6.022 \times 10^{23} \]\[ \text{number of N atoms} \approx 2.47 \times 10^{23} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Molar Mass Calculation
The molar mass of a substance is a key concept in chemistry that helps us bridge the gap between the microscopic world of atoms and molecules and the macroscopic world we can observe and measure. It gives us a way to convert between the amount of substance in moles and its mass in grams. To calculate the molar mass, sum up the atomic masses of all the atoms in a molecule:
  • Identify each type of atom in the molecule.
  • Multiply the atomic mass of each element by the number of atoms of that element in the molecule.
  • Add the masses of all the elements together to get the total molar mass.
For example, sucrose (C12H22O11) requires adding the atomic masses of 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms. Carbon has an atomic mass of 12.01 g/mol, hydrogen has 1.008 g/mol, and oxygen has 16.00 g/mol. When summed, these values provide the molar mass of sucrose as 342.30 g/mol.
Exploring Avogadro's Number
Avogadro's number, approximately 6.022 x 1023, is a fundamental constant in chemistry. It connects the amount of substance to the number of atoms or molecules present. Understanding Avogadro's number is crucial for converting between moles and molecules:
  • One mole of any substance contains exactly 6.022 x 1023 entities (atoms, molecules, etc.).
  • This immense number helps chemists work with quantities at the macroscopic scale, making it easier to handle bulk substances and perform precise calculations.
For instance, if you have 1.0 x 10-6 moles of ethanol (CH3CH2OH), using Avogadro's number will allow you to find out the exact number of ethanol molecules present. By multiplying the number of moles by Avogadro's number, you get approximately 6.022 x 1017 molecules.
Mastering Mass-to-Mole Conversion
Converting between mass and moles is a frequently used skill in chemistry that allows you to relate how much of a substance you have to how many moles it is, or vice versa. To perform a mass-to-mole conversion or its reverse, you'll apply these straightforward steps:
  • Determine the molar mass of the substance from the periodic table or a reference.
  • To find moles: Divide the mass of the substance (in grams) by its molar mass (g/mol).
  • To find mass from moles: Multiply the number of moles by the molar mass.
For example, let's calculate the moles of zinc nitrate (Zn(NO3)2) given 143.50 g of it. With a molar mass of 189.40 g/mol for zinc nitrate, dividing the mass by the molar mass yields approximately 0.757 moles.

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Most popular questions from this chapter

Epsom salts, a strong laxative used in veterinary medicine, is a hydrate, which means that a certain number of water molecules are included in the solid structure. The formula for Epsom salts can be written as \(\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O},\) where \(x\) indicates the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) per mole of \(\mathrm{MgSO}_{4}\). When \(5.061 \mathrm{~g}\) of this hydrate is heated to \(250^{\circ} \mathrm{C},\) all the water of hydration is lost, leaving \(2.472 \mathrm{~g}\) of \(\mathrm{MgSO}_{4}\). What is the value of \(x ?\)

What is the molecular formula of each of the following compounds? (a) empirical formula \(\mathrm{CH}_{3} \mathrm{O},\) molar mass \(=62.0 \mathrm{~g} / \mathrm{mol}\) (b) empirical formula \(\mathrm{NH}_{2}\), molar mass \(=32.0 \mathrm{~g} / \mathrm{mol}\)

The reaction between potassium superoxide, \(\mathrm{KO}_{2}\), and \(\mathrm{CO}_{2}\), $$ 4 \mathrm{KO}_{2}+2 \mathrm{CO}_{2} \longrightarrow 2 \mathrm{~K}_{2} \mathrm{CO}_{3}+3 \mathrm{O}_{2} $$ is used as a source of \(\mathrm{O}_{2}\) and absorber of \(\mathrm{CO}_{2}\) in selfcontained breathing equipment used by rescue workers. (a) How many moles of \(\mathrm{O}_{2}\) are produced when \(0.400 \mathrm{~mol}\) of \(\mathrm{KO}_{2}\) reacts in this fashion? (b) How many grams of \(\mathrm{KO}_{2}\) are needed to form \(7.50 \mathrm{~g}\) of \(\mathrm{O}_{2}\) ?

(a) One molecule of the antibiotic penicillin G has a mass of \(5.342 \times 10^{-21} \mathrm{~g}\). What is the molar mass of penicillin G? (b) Hemoglobin, the oxygen-carrying protein in red blood cells, has four iron atoms per molecule and contains \(0.340 \%\) iron by mass. Calculate the molar mass of hemoglobin.

Without doing any detailed calculations (but using a periodic table to give atomic weights), rank the following samples in order of increasing numbers of atoms: \(0.5 \mathrm{~mol} \mathrm{BCl}_{3}\) molecules, \(197 \mathrm{~g}\) gold, \(6.0 \times 10^{23} \mathrm{CCl}_{4}\) molecules.
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