Introduction to Chemistry Practice Midterm 1 – Step-by-Step Guidance

Q1. Which of these temperatures is the hottest?

Background

Topic: Temperature Scales and Conversions

This question tests your understanding of different temperature scales (Kelvin, Celsius, Fahrenheit) and how to compare temperatures across these scales.

Key Terms and Formulas:

• Kelvin (K): Absolute temperature scale.

• Celsius (°C): Water freezes at 0°C, boils at 100°C.

• Fahrenheit (°F): Water freezes at 32°F, boils at 212°F.

• Conversion formulas:

  • $T_{\text{C}} = \frac{5}{9}(T_{\text{F}} - 32)$

  • $T_{\text{K}} = T_{\text{C}} + 273.15$

Step-by-Step Guidance

1. Convert each temperature to the same scale (Celsius or Kelvin is usually easiest for comparison).

2. For (a) 200 K, convert to Celsius using $T_{\text{C}} = T_{\text{K}} - 273.15$.

3. For (b) -80°F, convert to Celsius using $T_{\text{C}} = \frac{5}{9}(T_{\text{F}} - 32)$.

4. For (c) -70°C, no conversion needed if comparing in Celsius.

5. Compare the three values to determine which is the highest (hottest).

Try solving on your own before revealing the answer!

Final Answer: b. -80 °F

When converted, -80°F is approximately -62°C, which is hotter than both 200 K (about -73°C) and -70°C.

Q2. Perform the following calculation and write your answer to the correct number of significant figures: $(7.20 \times 10^{-2} / 0.049) - 0.383$

Background

Topic: Significant Figures and Order of Operations

This question tests your ability to perform calculations with scientific notation and apply the rules for significant figures in division and subtraction.

Key Terms and Formulas:

• Significant figures: The number of meaningful digits in a value.

• Order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction (PEMDAS).

• Rules:

  • For multiplication/division: The result should have as many significant figures as the value with the fewest significant figures.

  • For addition/subtraction: The result should have as many decimal places as the value with the fewest decimal places.

Step-by-Step Guidance

1. First, divide $7.20 \times 10^{-2}$ by $0.049$.

2. Determine the number of significant figures for this division step.

3. Subtract $0.383$ from your result.

4. Apply the correct significant figure rules for subtraction (look at decimal places).

Try solving on your own before revealing the answer!

Final Answer: 1.1

The calculation yields approximately 1.095, which rounds to 1.1 with the correct significant figures.

Q3. Convert $1.187 \times 10^{-2}$ m³ to in³.

Background

Topic: Unit Conversions (Volume)

This question tests your ability to convert between metric and imperial units for volume, using appropriate conversion factors.

Key Terms and Formulas:

• 1 m = 39.3701 in

• 1 m³ = (39.3701 in)³ = 61,023.7 in³

• Conversion setup: $\text{value in in}^3 = \text{value in m}^3 \times \frac{61,023.7\ \text{in}^3}{1\ \text{m}^3}$

Step-by-Step Guidance

1. Write the given value: $1.187 \times 10^{-2}$ m³.

2. Multiply by the conversion factor $\frac{61,023.7\ \text{in}^3}{1\ \text{m}^3}$.

3. Set up the multiplication and check your significant figures (the given value has 4 significant figures).

4. Perform the multiplication, keeping track of significant figures, but do not calculate the final value yet.

Try solving on your own before revealing the answer!

Final Answer: 724.4 in³

Multiplying $1.187 \times 10^{-2}$ m³ by 61,023.7 in³/m³ gives 724.4 in³, rounded to 4 significant figures.

Q4. A metal has a density of 2.70 g/mL. An electrical wire with a diameter of 0.5 mm is made of that metal and has a volume of $3.00 \times 10^{-3}$ mL. What is the mass of the wire in mg?

Background

Topic: Density, Mass, and Unit Conversion

This question tests your ability to use the density formula to find mass, and to convert between grams and milligrams.

Key Terms and Formulas:

• Density formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Rearranged: $\text{Mass} = \text{Density} \times \text{Volume}$

• Unit conversion: $1\ \text{g} = 1000\ \text{mg}$

Step-by-Step Guidance

1. Write the given values: Density = 2.70 g/mL, Volume = $3.00 \times 10^{-3}$ mL.

2. Calculate the mass in grams using $\text{Mass} = \text{Density} \times \text{Volume}$.

3. Convert the mass from grams to milligrams by multiplying by 1000.

4. Check significant figures (both values have 3 significant figures).

Try solving on your own before revealing the answer!

Final Answer: 8.10 mg

The calculated mass is 0.00810 g, which is 8.10 mg when converted and rounded to 3 significant figures.

Q5. A particular atom has an atomic number of 16, an atomic mass of 34, and contains 18 electrons. a. What is the charge of the atom? b. What is the element symbol?

Background

Topic: Atomic Structure, Ions, and Element Identification

This question tests your understanding of atomic number, atomic mass, and how to determine the charge and identity of an atom based on its subatomic particles.

Key Terms and Formulas:

• Atomic number (Z): Number of protons, identifies the element.

• Atomic mass: Number of protons + neutrons.

• Charge: $\text{Charge} = \text{Number of protons} - \text{Number of electrons}$

Step-by-Step Guidance

1. Identify the number of protons (atomic number = 16).

2. Compare the number of protons (16) to the number of electrons (18) to determine the charge.

3. Use the periodic table to find the element with atomic number 16.

Try solving on your own before revealing the answer!

Final Answer:

a. Charge = -2

b. Element symbol = S (sulfur)

There are 2 more electrons than protons, so the charge is -2. Atomic number 16 corresponds to sulfur.

Q6. Which pair of atoms are isotopes of each other?

Background

Topic: Isotopes

This question tests your understanding of what makes two atoms isotopes: same number of protons, different number of neutrons.

Key Terms and Formulas:

• Isotopes: Atoms of the same element (same number of protons) with different numbers of neutrons.

Step-by-Step Guidance

1. For each pair, check if the number of protons is the same.

2. If so, check if the number of neutrons is different.

3. Identify which answer choice matches these criteria.

Try solving on your own before revealing the answer!

Final Answer: c. I and II

Both have 12 protons (same element), but different numbers of neutrons (12 and 14), so they are isotopes.

Q7. What is the formula mass of dinitrogen pentoxide?

Background

Topic: Formula Mass (Molecular Mass)

This question tests your ability to determine the formula mass of a compound by summing the atomic masses of all atoms in the formula.

Key Terms and Formulas:

• Formula mass: Sum of the atomic masses of all atoms in a molecule.

• Dinitrogen pentoxide: $N_2O_5$

• Atomic masses: N = 14.0 amu, O = 16.0 amu (rounded values)

Step-by-Step Guidance

1. Write the formula: $N_2O_5$.

2. Calculate the total mass of nitrogen: $2 \times 14.0$ amu.

3. Calculate the total mass of oxygen: $5 \times 16.0$ amu.

4. Add the two results to get the formula mass.

Try solving on your own before revealing the answer!

Final Answer: 108.0 amu

Adding $2 \times 14.0$ and $5 \times 16.0$ gives 108.0 amu for dinitrogen pentoxide.

Q8. If you have 5.0 Q/B³, how many M/Z³ do you have? Helpful information: 1 Q = 3.0 R, 2.0 B = 1 Z, 6.0 R = 1 M

Background

Topic: Dimensional Analysis (Unit Conversions)

This question tests your ability to use multiple conversion factors to convert a compound unit from one set of units to another.

Key Terms and Formulas:

• Dimensional analysis: Multiply by conversion factors to cancel units and convert to the desired units.

• Given conversion factors:

  • 1 Q = 3.0 R

  • 2.0 B = 1 Z

  • 6.0 R = 1 M

Step-by-Step Guidance

1. Start with 5.0 Q/B³.

2. Convert Q to R using $1\ Q = 3.0\ R$.

3. Convert R to M using $6.0\ R = 1\ M$.

4. Convert B³ to Z³ using $2.0\ B = 1\ Z$ (so $B^3$ to $Z^3$).

5. Set up the calculation with all conversion factors, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Final Answer: $2.0 \times 10^1$ M/Z³

After applying all conversion factors, you get $2.0 \times 10^1$ M/Z³.

Q9. Infants are to be given a medication at a dosage no higher than 15.0 mg/kg of body mass every 6 hours. What is the maximum total dosage a child weighing 18.0 lb should receive in a 12-hour period?

Background

Topic: Dosage Calculations and Unit Conversions

This question tests your ability to convert between pounds and kilograms, and to calculate total dosage over a given time period.

Key Terms and Formulas:

• 1 kg = 2.205 lb

• Dosage per 6 hours: 15.0 mg/kg

• Number of doses in 12 hours: 2

Step-by-Step Guidance

1. Convert 18.0 lb to kg using $1\ \text{kg} = 2.205\ \text{lb}$.

2. Calculate the maximum single dose using $15.0\ \text{mg/kg} \times \text{body mass in kg}$.

3. Multiply by the number of doses in 12 hours (2 doses).

4. Check significant figures throughout the calculation.

Try solving on your own before revealing the answer!

Final Answer: 245 mg

The child can receive a maximum total dosage of 245 mg in 12 hours.

Q10. What is the formula of ammonium phosphate, and how many hydrogen atoms are in it?

Background

Topic: Chemical Formulas and Counting Atoms

This question tests your ability to write the correct formula for a compound and count the number of specific atoms in one formula unit.

Key Terms and Formulas:

• Ammonium ion: $NH_4^+$

• Phosphate ion: $PO_4^{3-}$

• Formula for ammonium phosphate: Combine ions to balance charges.

Step-by-Step Guidance

1. Write the formulas for ammonium and phosphate ions.

2. Determine the ratio needed to balance the charges (3 ammonium ions for 1 phosphate ion).

3. Write the full formula for ammonium phosphate.

4. Count the number of hydrogen atoms in one formula unit.

Try solving on your own before revealing the answer!

Final Answer: $(NH_4)_3PO_4$, 12 H atoms

There are 3 ammonium ions, each with 4 hydrogens, for a total of 12 hydrogen atoms.

Q11. Choose the pair of name and formula that does NOT match.

Background

Topic: Naming Ionic Compounds

This question tests your ability to match chemical names with their correct formulas, focusing on transition metals and polyatomic ions.

Key Terms and Formulas:

• Roman numerals indicate the charge of the metal ion.

• Common polyatomic ions: nitrate ($NO_3^-$), sulfate ($SO_4^{2-}$), etc.

Step-by-Step Guidance

1. For each pair, check if the formula matches the name (especially the charge and the number of ions).

2. Pay special attention to the charges of the metal ions and the formulas of the anions.

3. Identify the pair that does not match.

Try solving on your own before revealing the answer!

Final Answer: d. chromium(III) sulfide: CrS

Chromium(III) has a +3 charge, but sulfide is -2, so the formula should not be CrS.

Q12. Which of the following is the correct equation for the ionization of aluminum?

Background

Topic: Ionization Equations

This question tests your understanding of how to write equations for the formation of ions from neutral atoms, including the correct number of electrons lost or gained.

Key Terms and Formulas:

• Ionization: The process by which an atom loses electrons to form a cation.

• Aluminum forms a $3^+$ ion by losing 3 electrons.

Step-by-Step Guidance

1. Recall that aluminum (Al) loses 3 electrons to form $Al^{3+}$.

2. Write the equation: $Al \rightarrow Al^{3+} + 3e^-$.

3. Compare this to the answer choices to find the correct one.

Try solving on your own before revealing the answer!

Final Answer: b. Al → Al³⁺ + 3e⁻

This equation correctly shows aluminum losing 3 electrons to form a $3^+$ ion.

Q13. Chlorine has two naturally occurring isotopes: Cl-35 (34.97 amu) and Cl-37 (36.97 amu). The atomic mass of chlorine is 35.45 amu. What is the relative abundance of each isotope in a naturally occurring sample?

Background

Topic: Average Atomic Mass and Isotopic Abundance

This question tests your ability to use the weighted average formula to determine the percent abundance of isotopes.

Key Terms and Formulas:

• Average atomic mass formula:

  • $\text{Average mass} = (\text{fraction}_{35} \times 34.97) + (\text{fraction}_{37} \times 36.97)$

  • $\text{fraction}_{35} + \text{fraction}_{37} = 1$

Step-by-Step Guidance

1. Let $x$ be the fraction of Cl-35, and $1-x$ be the fraction of Cl-37.

2. Set up the equation: $35.45 = (x \times 34.97) + ((1-x) \times 36.97)$.

3. Solve for $x$ (the fraction of Cl-35), then calculate $1-x$ for Cl-37.

4. Convert the fractions to percentages by multiplying by 100.

Try solving on your own before revealing the answer!

Final Answer: 76.0% Cl-35; 24.0% Cl-37

Cl-35 is 76.0% abundant, and Cl-37 is 24.0% in a natural sample.

Q14. How many protons, neutrons, and electrons are in the ion $^{56}Fe^{3+}$?

Background

Topic: Atomic Structure and Ions

This question tests your ability to determine the number of subatomic particles in an ion, given its atomic number, mass number, and charge.

Key Terms and Formulas:

• Protons: Equal to atomic number (Fe = 26).

• Neutrons: $\text{Mass number} - \text{Atomic number}$

• Electrons: For a cation, subtract the charge from the atomic number.

Step-by-Step Guidance

1. Find the atomic number of Fe (26 protons).

2. Calculate neutrons: $56 - 26$.

3. Calculate electrons: $26 - 3$ (since it's a $3^+$ ion).

Try solving on your own before revealing the answer!

Final Answer: 26 protons, 30 neutrons, 23 electrons

Fe has 26 protons, 56-26=30 neutrons, and 26-3=23 electrons for the $Fe^{3+}$ ion.

Q15. A sample of metal is either zinc or titanium. Fully submerged, it displaces 0.450 gal of water and weighs 16.85 lb. Which is it? (density of zinc = 7.13 g/cm³; density of titanium = 4.51 g/cm³)

Background

Topic: Density and Identification of Substances

This question tests your ability to use mass and volume to calculate density and compare it to known values to identify a substance.

Key Terms and Formulas:

• Density formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

• Unit conversions:

  • 1 gal = 3.785 L = 3785 cm³

  • 1 lb = 453.6 g

Step-by-Step Guidance

1. Convert the mass from pounds to grams: $16.85 \times 453.6$.

2. Convert the volume from gallons to cm³: $0.450 \times 3785$.

3. Calculate the density using $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$.

4. Compare your calculated density to the given densities for zinc and titanium to identify the metal.

Try solving on your own before revealing the answer!

Final Answer: b. titanium

The calculated density matches titanium (4.51 g/cm³) more closely than zinc.