Stoichiometry, Atomic Mass, and Chemical Equation Balancing Practice

Q1. Balance the following equation:

$\mathrm{C_8H_{18}O_3(l) + O_2(g) \rightarrow H_2O(g) + CO_2(g)}$

Background

Topic: Balancing Chemical Equations

This question tests your ability to balance a combustion reaction, ensuring the number of atoms of each element is the same on both sides of the equation.

Key Terms and Formulas:

• Reactants: $\mathrm{C_8H_{18}O_3}$ (an organic compound), $\mathrm{O_2}$ (oxygen gas)

• Products: $\mathrm{H_2O}$ (water vapor), $\mathrm{CO_2}$ (carbon dioxide)

• Balancing: Adjust coefficients to conserve atoms of C, H, and O.

Step-by-Step Guidance

1. Count the number of C, H, and O atoms in $\mathrm{C_8H_{18}O_3}$.

2. Assign coefficients to $\mathrm{CO_2}$ and $\mathrm{H_2O}$ to balance C and H atoms first.

3. Balance O atoms by adjusting the coefficient in front of $\mathrm{O_2}$.

4. Check all elements to ensure the equation is balanced.

Try solving on your own before revealing the answer!

Q2. A given element has two naturally occurring isotopes. One has mass = 6.0151 amu and abundance 7.5030%, and the other has mass = 7.0160 amu. What is the average atomic mass of this element?

Background

Topic: Isotopes and Average Atomic Mass

This question tests your understanding of how to calculate the weighted average atomic mass of an element based on the masses and abundances of its isotopes.

Key Terms and Formulas:

• Isotope: Atoms of the same element with different numbers of neutrons (and thus different masses).

• Average Atomic Mass Formula:

$\text{Average atomic mass} = (\text{fraction}_1 \times \text{mass}_1) + (\text{fraction}_2 \times \text{mass}_2)$

Step-by-Step Guidance

1. Convert the percent abundance to decimal (fractional) form for each isotope.

2. Multiply each isotope's mass by its fractional abundance.

3. Add the results to get the average atomic mass.

Try solving on your own before revealing the answer!

Q3. In a blast furnace, elemental iron is produced from a mixture of coke (C), iron ore ($\mathrm{Fe_3O_4}$), and other reactants. An important reaction sequence is:

$2\mathrm{C(s)} + \mathrm{O_2(g)} \rightarrow 2\mathrm{CO(g)}$ $\mathrm{Fe_3O_4(s)} + 4\mathrm{CO(g)} \rightarrow 3\mathrm{Fe(l)} + 4\mathrm{CO_2(g)}$

How many moles of iron can be formed in this sequence when 1.00 mol of carbon, as coke, is consumed?

Background

Topic: Stoichiometry in Multi-Step Reactions

This question tests your ability to use stoichiometry to relate the amount of a reactant (carbon) to the amount of product (iron) formed through a sequence of reactions.

Key Terms and Formulas:

• Stoichiometry: The calculation of reactants and products in chemical reactions using mole ratios from balanced equations.

• Mole Ratio: Use coefficients from the balanced equations to relate moles of C to moles of Fe.

Step-by-Step Guidance

1. From the first equation, determine how many moles of CO are produced per mole of C consumed.

2. Use the second equation to relate moles of CO to moles of Fe produced.

3. Set up the conversion: $1.00$ mol C $\rightarrow$ mol CO $\rightarrow$ mol Fe, using the appropriate mole ratios from the equations.

4. Multiply through the ratios to find the moles of Fe that can be produced from 1.00 mol C.