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Chapter 5: Problem 12

Calculate the number of millimoles contained in \(500 \mathrm{mg}\) of each of the following substances: (a) \(\mathrm{BaCrO}_{4},\) (b) \(\mathrm{CHCl}_{3}\), (c) \(\mathrm{KIO}_{3} \cdot \mathrm{HIO}_{3}\) (d) \(\mathrm{MgNH}_{4} \mathrm{PO}_{4}\), (e) \(\mathrm{Mg}_{2} \mathrm{P}_{2} \mathrm{O}_{7}\) (f) \(\mathrm{FeSO}_{4} \cdot \mathrm{C}_{2} \mathrm{H}_{4}\left(\mathrm{NH}_{3}\right)_{2} \mathrm{SO}_{4} \cdot 4 \mathrm{H}_{2} \mathrm{O}\)

Short Answer

Expert verified
a) 1.97 mmol, b) 4.19 mmol, c) 1.28 mmol, d) 3.64 mmol, e) 2.25 mmol, f) 1.27 mmol.

Step by step solution

01

Understanding Moles and Millimoles

Moles are a measure of the amount of substance, and one mole equals Avogadro's number ( 6.022 脳 10^{23} ) of particles or units. A mole can also be calculated by dividing the mass of the substance by its molar mass. Millimoles are smaller units where 1 mole equals 1000 millimoles.
02

Calculate Molar Mass

For a) BaCrO_{4} : Ba: 137.33, Cr: 51.996, O: 16.00 Total Molar Mass = 137.33 + 51.996 + (16.00 脳 4) = 253.33 g/mol b) CHCl_{3} : C: 12.01, H: 1.008, Cl: 35.453 Total Molar Mass = 12.01 + 1.008 + (35.453 脳 3) = 119.37 g/mol c) KIO_{3} 鈰� HIO_{3} : K: 39.098, I: 126.90, O: 16.00 Total Molar Mass = 39.098 + 126.90 + (16.00 脳 3) + 126.90 + (16.00 脳 3) = 389.86 g/mol d) MgNH_{4}PO_{4} : Mg: 24.305, N: 14.007, H: 1.008, P: 30.974, O: 16.00 Total Molar Mass = 24.305 + 14.007 + (1.008 脳 4) + 30.974 + (16.00 脳 4) = 137.32 g/mol e) Mg_{2}P_{2}O_{7} : Mg: 24.305, P: 30.974, O: 16.00 Total Molar Mass = (24.305 脳 2) + (30.974 脳 2) + (16.00 脳 7) = 222.548 g/mol f) FeSO_{4} 鈰� C_{2}H_{4}(NH_{3})_{2} SO_{4} 鈰� 4 H_{2}O : Fe: 55.845, S: 32.06, O: 16.00, C: 12.01, H: 1.008, N: 14.007 Total Molar Mass = 55.845 + 32.06 + (16.00 脳 4) + (12.01 脳 2) + (1.008 脳 4) + (14.007 脳 2) + 32.060 + (16.00 脳 4) + 4 脳 (2 脳 1.008 + 16.00) = 392.265 g/mol.
03

Convert Mass to Moles

The number of moles is calculated by dividing the mass of each substance (500 mg or 0.500 g) by their respective molar mass. a) BaCrO_{4} : rac{0.500}{253.33} = 0.00197 mol b) CHCl_{3} : rac{0.500}{119.37} = 0.00419 mol c) KIO_{3} 鈰� HIO_{3} : rac{0.500}{389.86} = 0.00128 mol d) MgNH_{4}PO_{4} : rac{0.500}{137.32} = 0.00364 mol e) Mg_{2}P_{2}O_{7} : rac{0.500}{222.548} = 0.00225 mol f) FeSO_{4} 鈰� C_{2}H_{4}(NH_{3})_{2} SO_{4} 鈰� 4 H_{2}O : rac{0.500}{392.265} = 0.00127 mol.
04

Convert Moles to Millimoles

To convert moles to millimoles, multiply the moles calculated in the previous step by 1000. a) BaCrO_{4} : 0.00197 imes 1000 = 1.97 mmol b) CHCl_{3} : 0.00419 imes 1000 = 4.19 mmol c) KIO_{3} 鈰� HIO_{3} : 0.00128 imes 1000 = 1.28 mmol d) MgNH_{4}PO_{4} : 0.00364 imes 1000 = 3.64 mmol e) Mg_{2}P_{2}O_{7} : 0.00225 imes 1000 = 2.25 mmol f) FeSO_{4} 鈰� C_{2}H_{4}(NH_{3})_{2} SO_{4} 鈰� 4 H_{2}O : 0.00127 imes 1000 = 1.27 mmol.

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Key Concepts

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

Molar Mass
Understanding the concept of molar mass is crucial when performing mole calculations. The molar mass of a substance is expressed in grams per mole (g/mol) and shows the weight of one mole of that substance. To determine the molar mass, you need to sum the atomic masses of all atoms within the chemical formula of the substance. These atomic masses are usually given in units of g/mol and can be found on the periodic table of elements. For instance, the molar mass of \( \mathrm{BaCrO}_4 \) is calculated as follows:
  • Barium (Ba) contributes 137.33 g/mol.
  • Chromium (Cr) adds 51.996 g/mol.
  • Oxygen (O) contributes \( 16.00 \times 4 = 64.00 \) g/mol.
By adding them, the total molar mass is 253.33 g/mol. This process is essential for converting the mass of a substance to moles, which is the next step for solving the exercise.
Millimoles
Millimoles, a smaller unit of measurement, are often used in chemistry to express quantities more conveniently when dealing with small mass samples. One mole is equal to 1000 millimoles, and this relationship is used to convert moles to millimoles by multiplying the number of moles by 1000.In the exercise, after calculating the moles of each substance, we then converted them to millimoles. For example, for \( \mathrm{BaCrO}_4 \),the moles obtained were \( 0.00197 \),which were then converted to millimoles as:\[ 0.00197 \times 1000 = 1.97 \text{ mmol} \] By using millimoles, chemists can conveniently express very small quantities, allowing for more precise calculations in laboratory settings.
Chemical Substances
Chemical substances are materials with a definite chemical composition. In this problem, we deal with various chemical substances, each with its own unique set of atoms. Each chemical formula like \( \mathrm{BaCrO}_{4}\) or \( \mathrm{CHCl}_{3}\) reveals the type and number of atoms present in the compound. Understanding how these are formulated is key to calculating molar masses.
  • Recognizing the individual components of a compound helps in breaking down and correctly calculating the molar mass.
  • Each chemical substance鈥檚 behavior can influence the calculations, especially methods like conversions to moles and millimoles.
This understanding facilitates accurate quantitative analysis necessary for theoretical and practical applications in chemistry.
Step-by-Step Solution
A clear step-by-step solution helps demystify complex chemical calculations. Here's a closer look:
  • Step 1: Identify the compounds and determine the molar mass for each using atomic masses from the periodic table.
  • Step 2: Convert the mass of the substance from milligrams to grams by dividing by 1000 (because 1 gram = 1000 milligrams).
  • Step 3: Use the molar mass to convert grams to moles via the formula:\[ \text{moles} = \frac{\text{mass in grams}}{\text{molar mass in g/mol}} \] This measures the quantity in moles.
  • Step 4: Convert the moles obtained to millimoles by multiplying by 1000.This systematic approach not only aids in solving the problem but also enhances understanding of the mole concept, mass conversion, and how chemists use these principles in laboratory and industrial settings. It allows learners to apply these skills to similar problems confidently.

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    Most popular questions from this chapter

    Calculate the molar concentrations of all the cations and anions in a solution prepared by mixing \(10.0 \mathrm{~mL}\) each of the following solutions: \(0.100 \mathrm{M} \mathrm{Mn}\left(\mathrm{NO}_{3}\right)_{2}, 0.100 M \mathrm{KNO}_{3},\) and \(0.100 M \mathrm{~K}, \mathrm{SO}_{4}\) \end{aligned}

    Calculate the grams of substance required to prepare the following solutions: (a) \(250 \mathrm{~mL}\) of \(5.00 \%\) (wt/vol) \(\mathrm{NaNO}_{3} ;\) (b) \(500 \mathrm{~mL}\) of \(1.00 \%\) (wt/vol) \(\mathrm{NH}_{4} \mathrm{NO}_{3},\) (c) \(1000 \mathrm{~mL}\) of \(10.0 \%\) (wt/vol) \(\mathrm{AgNO}_{3}\)

    Calculate the gravimetric factors for: $$ \begin{array}{cc} \hline \text { Substance Sought } & \text { Substance Weighed } \\ \hline \mathrm{Mn} & \mathrm{Mn}_{3} \mathrm{O}_{4} \\ \mathrm{Mn}_{2} \mathrm{O}_{3} & \mathrm{Mn}_{3} \mathrm{O}_{4} \\ \mathrm{Ag}_{2} \mathrm{~S} & \mathrm{BaSO}_{4} \\ \mathrm{CuCl}_{2} & \mathrm{AgCl} \\ \mathrm{MgI}_{2} & \mathrm{PbI}_{2} \\ \hline \end{array} $$

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