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Chapter 3: Problem 67

What amount (moles) is represented by each of these samples? a. 150.0 g Fe_ \(\mathrm{O}_{3}\) b. 10.0 \(\mathrm{mg} \mathrm{NO}_{2}\) c. \(1.5 \times 10^{16}\) molecules of \(\mathrm{BF}_{3}\)

Short Answer

Expert verified
a. \(0.939\) moles of Fe鈧侽鈧� b. \(2.17 \times 10^{-4}\) moles of NO鈧� c. \(2.49 \times 10^{-8}\) moles of BF鈧�

Step by step solution

01

Determine molar mass of each compound

We first need to determine the molar mass for each compound, using the periodic table. a. Fe鈧侽鈧� (Iron(III) oxide): Fe - 55.85 g/mol O - 16.00 g/mol Molar mass of Fe鈧侽鈧� = (2 x 55.85) + (3 x 16.00) = 111.70 + 48.00 = 159.70 g/mol b. NO鈧� (Nitrogen dioxide): N - 14.01 g/mol O - 16.00 g/mol Molar mass of NO鈧� = 14.01 + (2 x 16.00) = 14.01 + 32.00 = 46.01 g/mol c. BF鈧� (Boron trifluoride): B - 10.81 g/mol F - 19.00 g/mol Molar mass of BF鈧� = 10.81 + (3 x 19.00) = 10.81 + 57.00 = 67.81 g/mol
02

Convert mass to moles

Now that we have the molar mass for each compound, we can convert the given mass to moles using the formula: Moles = (Given mass) / (Molar mass) a. 150.0 g of Fe鈧侽鈧�: Moles of Fe鈧侽鈧� = 150.0 g / 159.70 g/mol = 0.939 moles b. 10.0 mg of NO鈧�: First, we need to convert milligrams to grams: 10 mg = 10 脳 10鈦宦� g = 0.010 g Moles of NO鈧� = 0.010 g / 46.01 g/mol = 2.17 脳 10鈦烩伌 moles c. 1.5 脳 10鹿鈦� molecules of BF鈧�: In this case, the substance is given in molecules and not in mass. We will use Avogadro's number (6.022 脳 10虏鲁) to convert it to moles: Moles = (Given molecules) / (Avogadro's number) Moles of BF鈧� = (1.5 脳 10鹿鈦�) / (6.022 脳 10虏鲁) = 2.49 脳 10鈦烩伕 moles Final answer: a. 0.939 moles of Fe鈧侽鈧� b. 2.17 脳 10鈦烩伌 moles of NO鈧� c. 2.49 脳 10鈦烩伕 moles of BF鈧�

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Key Concepts

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

Molar Mass Calculation
When figuring out how many moles of a substance you have, the first step is often determining its molar mass. Molar mass is how much one mole of that substance weighs in grams. Understanding this concept gives you the ability to switch from how much a substance weighs to how many particles of it you have, which is a key concept in chemistry.
To calculate molar mass, follow these steps:
  • Find the atomic mass of each element in the compound from the periodic table. This is usually a decimal number that represents grams per mole (g/mol).
  • Count how many atoms of each element are in the chemical formula.
  • Multiply the atomic mass by the number of atoms for each element to get the total mass for that element in the compound.
  • Add up all the total masses to get the compound's molar mass.
For example, to find the molar mass of Fe鈧侽鈧�:
  • Iron (Fe) has an atomic mass of 55.85 g/mol, and there are two Iron atoms. So, 2 x 55.85 = 111.70 g/mol.
  • Oxygen (O) has an atomic mass of 16.00 g/mol, and there are three Oxygen atoms. So, 3 x 16.00 = 48.00 g/mol.
  • Add these together: 111.70 + 48.00 = 159.70 g/mol.
This means that one mole of Fe鈧侽鈧� weighs 159.70 grams.
Mole Conversion
Once you have the molar mass of a compound, you can convert between the mass of a sample and the number of moles it contains. This is super helpful because reactions in chemistry happen in moles, not in grams. Here鈥檚 how you do it:
Use the formula:
  • Moles = \(\frac{\text{Given mass}}{\text{Molar mass}}\)
Consider different scenarios:
If you have a substance in grams and you need moles:
  • Divide the mass you have by the molar mass of the substance. This gives you the number of moles.
  • For example, with 150.0 g of Fe鈧侽鈧� and its molar mass being 159.70 g/mol, calculate moles as 150.0 / 159.70 = 0.939 moles.
If your sample is in a smaller unit like milligrams:
  • First convert to grams by dividing by 1000. Then use the same division with the molar mass.
  • For example, 10 mg of NO鈧� is 0.010 g because 10 mg = 10 x 10鈦宦� g. Then, moles are 0.010 / 46.01 = 2.17 x 10鈦烩伌 moles.
This conversion is essential for completing chemical reaction calculations in labs and homework.
Avogadro's Number
Avogadro's number is a key constant in chemistry: it allows you to convert the number of molecules into moles. It is denoted as \(6.022 \times 10^{23}\) and represents the number of units (atoms, molecules, ions, etc.) in one mole of a substance.
To convert molecules to moles:
  • Use the formula: Moles = \(\frac{\text{Given molecules}}{\text{Avogadro's number}}\)
  • For example, if you have \(1.5 \times 10^{16} \) molecules of BF鈧�, the calculation is \( \frac{1.5 \times 10^{16}}{6.022 \times 10^{23}} = 2.49 \times 10^{-8} \) moles.
Understanding Avogadro's number provides insight into the scale at which chemistry operates鈥攂ridging macroscopic scales (like grams) with the vast number of tiny particles each mole contains. This bridge is crucial for predicting and measuring chemical reactions and understanding material properties.

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Most popular questions from this chapter

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