Problem 127 - Introductory Chemistry Atoms First

Question

Chrome yellow, a pigment used in paints, is \(64.11 \%\) by mass \(\mathrm{Pb}, 16.09 \%\) by mass \(\mathrm{Cr}\), and \(19.80 \%\) by mass O. What is the empirical formula of this compound?

Step-by-Step Solution

Answer

The empirical formula of chrome yellow pigment, which consists of 64.11% lead (Pb), 16.09% chromium (Cr), and 19.80% oxygen (O) by mass, is \(PbCrO_4\).

Step 1: Convert percentages to mass

We can assume that there is 100 g of the pigment, as the given percentages will directly correspond to the mass in grams. Therefore, we have: - 64.11 g of lead (Pb) - 16.09 g of chromium (Cr) - 19.80 g of oxygen (O)

Step 2: Convert mass to moles

To convert the mass of each element into moles, we should divide its mass by its molar mass. - The molar mass of Pb is \(207.2 g/mol\) - The molar mass of Cr is \(51.996 g/mol\) - The molar mass of O is \(16.00 g/mol\) Moles of Pb = \(\frac{64.11}{207.2} = 0.3091 \:mol\) Moles of Cr = \(\frac{16.09}{51.996} = 0.3091 \:mol\) Moles of O = \(\frac{19.80}{16.00} = 1.2375 \:mol\)

Step 3: Find the smallest whole number ratio

Divide each moles value by the smallest moles value (0.3091). This gives: - Moles of Pb: \(\frac{0.3091}{0.3091} = 1\) - Moles of Cr: \(\frac{0.3091}{0.3091} = 1\) - Moles of O: \(\frac{1.2375}{0.3091} = 4\) Thus, the smallest whole number ratio is Pb:Cr:O = 1:1:4

Step 4: Write the empirical formula

The empirical formula of this compound is: \(Pb_1Cr_1O_4 \), which can be simplified to: \(PbCrO_4\) So, the empirical formula of chrome yellow pigment is \(PbCrO_4\).

Key Concepts

Molar Mass

The molar mass of an element or compound is a fundamental concept in chemistry. It represents the mass of one mole of the substance, usually expressed in grams per mole (\(g/mol\)). Understanding how to calculate molar mass is crucial when determining the composition of compounds.

To find the molar mass of an element like lead (Pb) or chromium (Cr), you can refer to the periodic table, where each element's mass is listed. For example:

• The molar mass of lead (Pb) is \(207.2 \) g/mol.
• The molar mass of chromium (Cr) is \(51.996\) g/mol.
• Oxygen (O) has a molar mass of \(16.00\) g/mol.

By knowing the molar mass, you can convert grams to moles, which is integral in analyzing chemical compositions.

Mole Conversion

Mole conversion is a method used to convert mass in grams to moles, a fundamental step in chemistry calculations. This process involves dividing the mass of a substance by its molar mass.

For example, if you have 64.11 grams of lead (Pb), and you wish to find how many moles this represents, you would compute:

• Moles of Pb = \(\frac{64.11}{207.2} = 0.3091 \ mol\).
• Similarly, for chromium (Cr): Moles of Cr = \(\frac{16.09}{51.996} = 0.3091 \ mol\).
• And for oxygen (O): Moles of O = \(\frac{19.80}{16.00} = 1.2375 \ mol\).

These conversions allow chemists to compare amount of substances, leading to determination of proportions in chemical formulas.

Whole Number Ratio

Chemistry often requires finding the simplest whole number ratio of elements present in a compound, which relates directly to empirical formulas. To derive this ratio, divide the moles of each element by the smallest number of moles calculated in your findings.

For example, if you calculated:

• Moles of Pb: \(\frac{0.3091}{0.3091} = 1\)
• Moles of Cr: \(\frac{0.3091}{0.3091} = 1\)
• Moles of O: \(\frac{1.2375}{0.3091} \approx 4\)

This results in a ratio of Pb:Cr:O = 1:1:4. Achieving these whole numbers is key to writing the empirical formula, ensuring it accurately reflects the composition without fractional numbers.

Chromium Compounds

Chromium compounds, including those like Chrome Yellow (\(PbCrO_4\)), are widely used in various industries. They are valued for their vibrant colors and are often used as pigments in paints, ceramics, and plastics.

Crucial properties of chromium compounds include:

• High melting points.
• The presence of vivid coloration, often used in dyes and pigments.
• Applications in corrosion resistance when used in metal alloys.

To identify chromium compounds in a lab setting, analyzing the molecular composition using tools like empirical formula calculations helps determine the compound's exact makeup, paving the way for further application in various fields.