Question

Using the average atomic masses given inside the front cover of this text, calculate how many moles of each element the following masses represent. a. \(1.5 \mathrm{mg}\) of chromium b. \(2.0 \times 10^{-3} \mathrm{g}\) of strontium c. \(4.84 \times 10^{4}\) g of boron d. \(3.6 \times 10^{-6} \mu g\) of californium e. 1.0 ton \((2000\) lb) of iron f. \(20.4 \mathrm{g}\) of barium g. \(62.8 \mathrm{g}\) of cobalt

Short answer

The number of moles for each element are as follows: a. Chromium: \(2.88 \times 10^{-5}\, \mathrm{mol}\) b. Strontium: \(2.28 \times 10^{-5}\, \mathrm{mol}\) c. Boron: \(4.48 \times 10^{3}\, \mathrm{mol}\) d. Californium: \(1.435 \times 10^{-17}\, \mathrm{mol}\) e. Iron: \(16236\, \mathrm{mol}\) f. Barium: \(0.149\, \mathrm{mol}\) g. Cobalt: \(1.065\, \mathrm{mol}\)

Step-by-step solution

Write the given mass and atomic mass of chromium in grams

Given mass of chromium = \(1.5\, \mathrm{mg}\) (convert this to grams) Average atomic mass of chromium = \(\approx 51.996\, \mathrm{g/mol}\) b. Strontium

Write the given mass and atomic mass of strontium in grams

Given mass of strontium = \(2.0 \times 10^{-3} \mathrm{g}\) Average atomic mass of strontium = \(\approx 87.62\, \mathrm{g/mol}\) c. Boron

Write the given mass and atomic mass of boron in grams

Given mass of boron = \(4.84 \times 10^{4} \mathrm{g}\) Average atomic mass of boron = \(\approx 10.81\, \mathrm{g/mol}\) d. Californium

Write the given mass and atomic mass of californium in grams

Given mass of californium = \(3.6 \times 10^{-6} \mu \mathrm{g}\) (convert this to grams) Average atomic mass of californium = \(\approx 251\, \mathrm{g/mol}\) e. Iron

Write the given mass and atomic mass of iron in grams

Given mass of iron = \(1.0\, \mathrm{ton}\) (convert this to grams) Average atomic mass of iron = \(\approx 55.845\, \mathrm{g/mol}\) f. Barium

Write the given mass and atomic mass of barium in grams

Given mass of barium = \(20.4 \mathrm{g}\) Average atomic mass of barium = \(\approx 137.33\, \mathrm{g/mol}\) g. Cobalt

Write the given mass and atomic mass of cobalt in grams

Given mass of cobalt = \(62.8 \mathrm{g}\) Average atomic mass of cobalt = \(\approx 58.933\, \mathrm{g/mol}\) Now we will find the number of moles for each element using the formula in the analysis section. a. Chromium

Calculate the number of moles of chromium

Number of moles = \(\frac{1.5\, \mathrm{mg}}{51.996\, \mathrm{g/mol}} = \frac{0.0015\, \mathrm{g}}{51.996\, \mathrm{g/mol}} \approx 2.88 \times 10^{-5}\, \mathrm{mol}\) b. Strontium

Calculate the number of moles of strontium

Number of moles = \(\frac{2.0 \times 10^{-3} \mathrm{g}}{87.62\, \mathrm{g/mol}} \approx 2.28 \times 10^{-5}\, \mathrm{mol}\) c. Boron

Calculate the number of moles of boron

Number of moles = \(\frac{4.84 \times 10^{4} \mathrm{g}}{10.81\, \mathrm{g/mol}} \approx 4.48 \times 10^{3}\, \mathrm{mol}\) d. Californium

Calculate the number of moles of californium

Number of moles = \(\frac{3.6 \times 10^{-6} \mu \mathrm{g}}{251\, \mathrm{g/mol}} = \frac{3.6 \times 10^{-15} \mathrm{g}}{251\, \mathrm{g/mol}} \approx 1.435 \times 10^{-17}\, \mathrm{mol}\) e. Iron

Calculate the number of moles of iron

Number of moles = \(\frac{1.0\, \mathrm{ton}}{55.845\, \mathrm{g/mol}} = \frac{907184.74\, \mathrm{g}}{55.845\, \mathrm{g/mol}} \approx 16236\, \mathrm{mol}\) f. Barium

Calculate the number of moles of barium

Number of moles = \(\frac{20.4 \mathrm{g}}{137.33\, \mathrm{g/mol}} \approx 0.149\, \mathrm{mol}\) g. Cobalt

Calculate the number of moles of cobalt

Number of moles = \(\frac{62.8 \mathrm{g}}{58.933\, \mathrm{g/mol}} \approx 1.065\, \mathrm{mol}\) The number of moles for each element has been calculated using the given masses and the average atomic masses.

Key concepts

Atomic Mass Conversion

Understanding the concept of atomic mass is crucial in chemistry, especially when dealing with tiny particles like atoms. Atomic mass is the mass of an atom expressed in atomic mass units (amu), but in the context of chemical calculations, it's frequently converted to units of grams per mole. This conversion allows us to connect the atomic scale with the macroscopic amounts used in the lab or industry.

To perform an atomic mass conversion:

• Find the element's atomic mass, typically provided in grams per mole (g/mol).
• This value is used as a conversion factor in calculations to transition from atomic or subatomic world measurements (like mg or µg) to a more tangible mass in grams or kilograms.
• This conversion is essential for understanding how much of an element you're working with in chemical reactions.

For instance, when given a mass in milligrams (mg), you must first convert this mass to grams. Simply move the decimal point three places to the left (since 1 mg = 0.001 g). This step is fundamental in preparing for subsequent calculations.

Mass to Moles Calculation

Once you have the mass of a substance in grams and you know the atomic mass in g/mol, the next step is to calculate the number of moles. Moles are a standard unit in chemistry for expressing amounts of a substance, facilitating the balance of chemical equations and the study of reaction stoichiometry.

The formula used here is:
\[\text{Number of Moles} = \frac{\text{Mass in grams}}{\text{Atomic Mass in g/mol}}\]
Let's break it down:

• Divide the mass you have (after conversion to grams) by the atomic mass of the element.
• This division cancels out the grams, leaving you with moles, revealing how many particles of the element you're dealing with on an atomic level.

This method is universally applicable to all elements in the periodic table, allowing for seamless transitions from mass to the more abstract concept of moles.

Chemistry Problem Solving

Chemistry problem solving often involves understanding and applying concepts like atomic mass conversion and mass to moles calculation. These fundamental skills are the foundation for more complex problem-solving tasks in chemistry, such as balancing equations, reaction yield predictions, and concentration calculations.

Here's a layout on how to approach these problems effectively:

• **Read the Problem:** Thoroughly understand what is being asked. Identify the knowns and unknowns.
  
  
• **Set Up the Conversion:** Convert all given quantities to the necessary units (e.g., mg to g) using appropriate conversion factors.
  
  
• **Calculate Moles:** Use the mass converted to grams and apply the formula to calculate moles.
  
  
• **Cross-check Units:** Ensure units are consistent across calculations to prevent errors.

By mastering these steps, students can enhance their chemistry problem-solving skills and approach exercises with confidence.