Step-by-Step Guidance for CHEMISTRY 106 Exam 1 Study Guide

Q1. How many significant figures are in 0.00450?

Background

Topic: Significant Figures

This question tests your understanding of how to count significant figures in a measured value, which is important for reporting scientific data accurately.

Key Terms:

• Significant figures: Digits in a number that are meaningful in terms of accuracy.

• Leading zeros: Zeros before the first nonzero digit; not significant.

• Trailing zeros: Zeros after the decimal point and after a nonzero digit; significant.

Step-by-Step Guidance

1. Identify all digits in the number: 0.00450.

2. Determine which zeros are leading (before the first nonzero digit) and which are trailing (after the decimal and after a nonzero digit).

3. Apply the rules: Leading zeros are not significant; zeros between nonzero digits and trailing zeros after a decimal are significant.

Try solving on your own before revealing the answer!

Final Answer: 3 significant figures

The digits 4, 5, and the trailing zero are all significant. Leading zeros are not counted.

Q2. Calculate: (3.45 × 2.1) with correct significant figures.

Background

Topic: Significant Figures in Multiplication

This question tests your ability to apply significant figure rules when multiplying measured values.

Key Terms:

• Multiplication rule: The result should have the same number of significant figures as the factor with the fewest significant figures.

Step-by-Step Guidance

1. Count the significant figures in each number: 3.45 (3 sig figs), 2.1 (2 sig figs).

2. Multiply the numbers: $3.45 \times 2.1$.

3. Round the result to the correct number of significant figures (the smallest count from the factors).

Try solving on your own before revealing the answer!

Final Answer: 7.2

The product is rounded to 2 significant figures, matching the least precise factor.

Q3. Calculate: 12.11 + 0.3 with correct significant figures.

Background

Topic: Significant Figures in Addition

This question tests your ability to apply significant figure rules when adding measured values.

Key Terms:

• Addition rule: The result should be rounded to the same decimal place as the least precise measurement.

Step-by-Step Guidance

1. Identify the decimal places in each number: 12.11 (hundredths), 0.3 (tenths).

2. Add the numbers: $12.11 + 0.3$.

3. Round the result to the least precise decimal place (tenths).

Try solving on your own before revealing the answer!

Final Answer: 12.4

The sum is rounded to the tenths place, matching the least precise measurement.

Q4. Convert 5.25 miles to kilometers.

Background

Topic: Dimensional Analysis

This question tests your ability to use conversion factors to change units from miles to kilometers.

Key Terms and Formulas:

• Dimensional analysis: Method for converting units using conversion factors.

• Common conversion factors: $1 \text{ mile} = 1.609 \text{ km}$

Step-by-Step Guidance

1. Write the given value: $5.25 \text{ miles}$.

2. Set up the conversion factor: $1 \text{ mile} = 1.609 \text{ km}$.

3. Multiply the given value by the conversion factor to cancel miles and obtain kilometers.

Try solving on your own before revealing the answer!

Final Answer: 8.45 km

$5.25 \times 1.609 = 8.45$ km (rounded to 3 significant figures).

Q5. Convert 45.0 g to kilograms.

Background

Topic: Dimensional Analysis

This question tests your ability to convert mass units from grams to kilograms.

Key Terms and Formulas:

• Conversion factor: $1 \text{ kg} = 1000 \text{ g}$

Step-by-Step Guidance

1. Write the given value: $45.0 \text{ g}$.

2. Set up the conversion factor: $1 \text{ kg} = 1000 \text{ g}$.

3. Multiply the given value by the conversion factor to cancel grams and obtain kilograms.

Try solving on your own before revealing the answer!

Final Answer: 0.0450 kg

$45.0 \div 1000 = 0.0450$ kg (rounded to 3 significant figures).

Q6. Convert 2.50 hours to seconds.

Background

Topic: Dimensional Analysis

This question tests your ability to convert time units from hours to seconds using multiple conversion factors.

Key Terms and Formulas:

• $1 \text{ hour} = 60 \text{ minutes}$

• $1 \text{ minute} = 60 \text{ seconds}$

Step-by-Step Guidance

1. Write the given value: $2.50 \text{ hours}$.

2. Convert hours to minutes: $2.50 \times 60$.

3. Convert minutes to seconds: Multiply the result by 60.

Try solving on your own before revealing the answer!

Final Answer: 9000 s

$2.50 \times 60 \times 60 = 9000$ seconds.

Q7. A sample has a mass of 25.0 g and volume of 10.0 mL. What is the density?

Background

Topic: Density Calculation

This question tests your ability to calculate density from mass and volume.

Key Formula:

$\text{Density} = \frac{\text{mass}}{\text{volume}}$

Step-by-Step Guidance

1. Write the given values: mass = 25.0 g, volume = 10.0 mL.

2. Plug the values into the density formula: $\text{Density} = \frac{25.0}{10.0}$.

3. Calculate the result and consider significant figures.

Try solving on your own before revealing the answer!

Final Answer: 2.50 g/mL

Both values have 3 significant figures, so the answer should as well.

Q8. A metal has density 8.96 g/mL. What mass is 15.0 mL?

Background

Topic: Density Calculation

This question tests your ability to use density to find mass given volume.

Key Formula:

$\text{mass} = \text{density} \times \text{volume}$

Step-by-Step Guidance

1. Write the given values: density = 8.96 g/mL, volume = 15.0 mL.

2. Plug the values into the formula: $\text{mass} = 8.96 \times 15.0$.

3. Calculate the result and consider significant figures.

Try solving on your own before revealing the answer!

Final Answer: 134 g

Answer rounded to 3 significant figures.

Q9. Two samples of a compound contain 4.0 g O and 2.0 g H; another has 8.0 g O and 4.0 g H. Does this obey definite proportions?

Background

Topic: Law of Definite Proportions

This question tests your understanding of whether a compound always contains the same elements in the same ratio by mass.

Key Terms:

• Law of Definite Proportions: A chemical compound always contains the same proportion of elements by mass.

Step-by-Step Guidance

1. Calculate the mass ratio of O to H in each sample: $\frac{4.0}{2.0}$ and $\frac{8.0}{4.0}$.

2. Compare the ratios to see if they are the same.

Try solving on your own before revealing the answer!

Final Answer: Yes, the ratios are the same

Both samples have a 2:1 ratio of O to H, so they obey the law of definite proportions.

Q10. Compound A has 1.0 g N reacting with 2.0 g O. Compound B has 1.0 g N reacting with 4.0 g O. Does this obey multiple proportions?

Background

Topic: Law of Multiple Proportions

This question tests your understanding of whether two compounds formed from the same elements have mass ratios that are simple whole numbers.

Key Terms:

• Law of Multiple Proportions: When two elements form more than one compound, the ratios of the masses of the second element that combine with a fixed mass of the first element are simple whole numbers.

Step-by-Step Guidance

1. Fix the mass of N (1.0 g) and compare the mass of O in each compound: 2.0 g and 4.0 g.

2. Calculate the ratio of O masses: $\frac{4.0}{2.0}$.

3. Determine if the ratio is a simple whole number.

Try solving on your own before revealing the answer!

Final Answer: Yes, ratio is 2:1

The ratio of O masses is a simple whole number, so it obeys the law of multiple proportions.

Q11. An element has two isotopes: 60% at 10 amu and 40% at 11 amu. Calculate atomic mass.

Background

Topic: Weighted Average Atomic Mass

This question tests your ability to calculate the average atomic mass using isotope abundances and masses.

Key Formula:

$\text{Atomic mass} = \sum (\text{fractional abundance} \times \text{isotope mass})$

Step-by-Step Guidance

1. Convert percentages to fractions: 60% = 0.60, 40% = 0.40.

2. Multiply each fraction by its isotope mass: $0.60 \times 10$ and $0.40 \times 11$.

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

Try solving on your own before revealing the answer!

Final Answer: 10.4 amu

$0.60 \times 10 + 0.40 \times 11 = 10.4$ amu.

Q12. How many moles are in 36.0 g of H2O?

Background

Topic: Mole Conversions

This question tests your ability to convert mass to moles using molar mass.

Key Formula:

$\text{moles} = \frac{\text{mass}}{\text{molar mass}}$

Step-by-Step Guidance

1. Find the molar mass of H2O: $2 \times 1.01 + 16.00 = 18.02$ g/mol.

2. Plug the values into the formula: $\frac{36.0}{18.02}$.

3. Calculate the result and consider significant figures.

Try solving on your own before revealing the answer!

Final Answer: 2.00 mol

$36.0 \div 18.02 = 2.00$ mol (rounded to 3 significant figures).

Q13. How many atoms are in 0.50 moles of carbon?

Background

Topic: Mole Conversions

This question tests your ability to convert moles to number of atoms using Avogadro's number.

Key Formula:

$\text{atoms} = \text{moles} \times 6.022 \times 10^{23}$

Step-by-Step Guidance

1. Write the given value: 0.50 moles.

2. Multiply by Avogadro's number: $0.50 \times 6.022 \times 10^{23}$.

3. Calculate the result and consider significant figures.

Try solving on your own before revealing the answer!

Final Answer: $3.0 \times 10^{23}$ atoms

Answer rounded to 2 significant figures.

Q14. How many atoms are in 12.0 g of magnesium?

Background

Topic: Mole Conversions

This question tests your ability to convert mass to moles, then moles to atoms.

Key Formulas:

• $\text{moles} = \frac{\text{mass}}{\text{molar mass}}$

• $\text{atoms} = \text{moles} \times 6.022 \times 10^{23}$

Step-by-Step Guidance

1. Find the molar mass of Mg: 24.31 g/mol.

2. Calculate moles: $\frac{12.0}{24.31}$.

3. Multiply the moles by Avogadro's number to get atoms.

Try solving on your own before revealing the answer!

Final Answer: $2.97 \times 10^{23}$ atoms

Answer rounded to 3 significant figures.

Q15. What is the frequency of light with wavelength 500 nm?

Background

Topic: Electromagnetic Radiation

This question tests your ability to relate wavelength and frequency using the speed of light.

Key Formula:

$c = \lambda \nu$

• $c$ = speed of light ($3.00 \times 10^8$ m/s)

• $\lambda$ = wavelength (in meters)

• $\nu$ = frequency (in Hz)

Step-by-Step Guidance

1. Convert wavelength from nm to meters: $500 \text{ nm} = 5.00 \times 10^{-7}$ m.

2. Use the formula: $\nu = \frac{c}{\lambda}$.

3. Plug in the values: $\nu = \frac{3.00 \times 10^8}{5.00 \times 10^{-7}}$.

Try solving on your own before revealing the answer!

Final Answer: $6.00 \times 10^{14}$ Hz

Frequency calculated using the speed of light and wavelength.

Q16. Calculate the energy of a photon with wavelength 400 nm.

Background

Topic: Electromagnetic Radiation

This question tests your ability to calculate photon energy using wavelength.

Key Formula:

$E = \frac{hc}{\lambda}$

• $h$ = Planck's constant ($6.626 \times 10^{-34}$ J·s)

• $c$ = speed of light ($3.00 \times 10^8$ m/s)

• $\lambda$ = wavelength (in meters)

Step-by-Step Guidance

1. Convert wavelength from nm to meters: $400 \text{ nm} = 4.00 \times 10^{-7}$ m.

2. Plug values into the formula: $E = \frac{(6.626 \times 10^{-34})(3.00 \times 10^8)}{4.00 \times 10^{-7}}$.

3. Calculate the result and consider significant figures.

Try solving on your own before revealing the answer!

Final Answer: $4.97 \times 10^{-19}$ J

Energy calculated using Planck's constant, speed of light, and wavelength.

Q17. Calculate the wavelength of an electron moving at $2.0 \times 10^6$ m/s.

Background

Topic: De Broglie Equation

This question tests your ability to calculate the wavelength of a particle using its mass and velocity.

Key Formula:

$\lambda = \frac{h}{mv}$

• $h$ = Planck's constant ($6.626 \times 10^{-34}$ J·s)

• $m$ = mass of electron ($9.11 \times 10^{-31}$ kg)

• $v$ = velocity ($2.0 \times 10^6$ m/s)

Step-by-Step Guidance

1. Write the values for $h$, $m$, and $v$.

2. Plug into the formula: $\lambda = \frac{6.626 \times 10^{-34}}{(9.11 \times 10^{-31})(2.0 \times 10^6)}$.

3. Calculate the result and consider significant figures.

Try solving on your own before revealing the answer!

Final Answer: $3.6 \times 10^{-10}$ m

Wavelength calculated using De Broglie equation.

Q18. Calculate energy change for electron from n=3 to n=2 in hydrogen.

Background

Topic: Bohr Model

This question tests your ability to calculate energy changes for electron transitions in hydrogen.

Key Formulas:

• $E_n = -2.18 \times 10^{-18} \left(\frac{1}{n^2}\right)$ J

• $\Delta E = E_{\text{final}} - E_{\text{initial}}$

Step-by-Step Guidance

1. Calculate $E_{\text{final}}$ for $n=2$ and $E_{\text{initial}}$ for $n=3$ using the formula.

2. Subtract $E_{\text{initial}}$ from $E_{\text{final}}$ to find $\Delta E$.

3. Consider the sign of $\Delta E$ (negative means energy is emitted).

Try solving on your own before revealing the answer!

Final Answer: $-2.86 \times 10^{-19}$ J

Energy is emitted as the electron moves from n=3 to n=2.

Q19. Is energy absorbed or emitted for n=2 to n=5?

Background

Topic: Bohr Model

This question tests your understanding of electron transitions and whether energy is absorbed or emitted.

Key Concept:

• Moving to a higher n (energy level) requires energy absorption.

• Moving to a lower n releases energy (emission).

Step-by-Step Guidance

1. Identify the direction of the transition: n=2 to n=5 is upward (higher energy).

2. Recall that upward transitions require energy absorption.

Try solving on your own before revealing the answer!

Final Answer: Energy is absorbed

Electron moves to a higher energy level, so energy is absorbed.

Q20. If photon energy is $5.0 \times 10^{-19}$ J and binding energy is $3.0 \times 10^{-19}$ J, what is KE?

Background

Topic: Photoelectric Effect

This question tests your ability to calculate the kinetic energy of an ejected electron.

Key Formula:

$\text{KE} = E_{\text{photon}} - E_{\text{binding}}$

Step-by-Step Guidance

1. Write the given values: $E_{\text{photon}} = 5.0 \times 10^{-19}$ J, $E_{\text{binding}} = 3.0 \times 10^{-19}$ J.

2. Plug into the formula: $\text{KE} = 5.0 \times 10^{-19} - 3.0 \times 10^{-19}$.

3. Calculate the result and consider significant figures.

Try solving on your own before revealing the answer!

Final Answer: $2.0 \times 10^{-19}$ J

Kinetic energy is the difference between photon and binding energy.

Q21. If n = 3, list all possible values of l.

Background

Topic: Quantum Numbers

This question tests your understanding of the allowed values for the angular momentum quantum number l given a principal quantum number n.

Key Terms:

• n: Principal quantum number (positive integer)

• l: Angular momentum quantum number (0 to n−1)

Step-by-Step Guidance

1. For n = 3, l can be any integer from 0 up to n−1.

2. List all possible values: 0, 1, 2.

Try solving on your own before revealing the answer!

Final Answer: l = 0, 1, 2

For n = 3, l can be 0, 1, or 2.

Q22. If l = 2, list all possible values of ml.

Background

Topic: Quantum Numbers

This question tests your understanding of the allowed values for the magnetic quantum number ml given a value of l.

Key Terms:

• l: Angular momentum quantum number

• ml: Magnetic quantum number (−l to +l)

Step-by-Step Guidance

1. For l = 2, ml can be any integer from −2 to +2.

2. List all possible values: −2, −1, 0, 1, 2.

Try solving on your own before revealing the answer!

Final Answer: ml = −2, −1, 0, 1, 2

For l = 2, ml can be −2, −1, 0, 1, or 2.