Show Your Calculations For Each Of The Following. Remember, Calculations Should Follow The Rules For Significant Figures.Use The Balanced Chemical Reaction: ${ 2 \text{Mg} {(s)} + \text{O} {2(g)} \rightarrow 2 \text{MgO}_{(s)} }$1. Subtract

Mar 13, 2025 by ADMIN 242 views

**Significant Figures in Chemical Calculations**

=====================================================

Understanding Significant Figures

Significant figures are an essential concept in chemistry, as they help us determine the accuracy and precision of our measurements and calculations. In this article, we will explore the rules for significant figures and apply them to a balanced chemical reaction.

Rules for Significant Figures

The rules for significant figures are as follows:

Non-zero numbers: All non-zero numbers have at least one significant figure.
Zeros between non-zero numbers: Zeros between non-zero numbers are significant.
Zeros at the end of a number: Zeros at the end of a number are significant only if the number contains a decimal point.
Zeros at the beginning of a number: Zeros at the beginning of a number are not significant.
Rounding: When rounding a number, we look at the first non-significant digit (the digit after the last significant digit). If it is 5 or greater, we round up; if it is less than 5, we round down.

Balanced Chemical Reaction

The balanced chemical reaction is:

${ 2 \text{Mg}_{(s)} + \text{O}_{2(g)} \rightarrow 2 \text{MgO}_{(s)} }$

Calculations

1. Subtract 0.500 g of Mg from 2.50 g of Mg

To subtract 0.500 g of Mg from 2.50 g of Mg, we need to follow the rules for significant figures.

# Define the variables
m1 = 2.50  # initial mass of Mg in g
m2 = 0.500  # mass of Mg to be subtracted in g
m_result = m1 - m2

print(f"The result of the subtraction is {m_result} g")

The result of the subtraction is 1.99 g. Since the result has only two significant figures, we can round it to 2.0 g.

2. Calculate the number of moles of MgO produced

To calculate the number of moles of MgO produced, we need to know the molar mass of MgO. The molar mass of MgO is 40.30 g/mol.

# Define the variables
m_mgo = 40.30  # molar mass of MgO in g/mol
m_result = 2.00  # mass of MgO produced in g

n_mgo = m_result / m_mgo

print(f"The number of moles of MgO produced is {n_mgo} mol")

The number of moles of MgO produced is 0.0497 mol. Since the result has only three significant figures, we can round it to 0.050 mol.

3. Calculate the number of moles of O2 consumed

To calculate the number of moles of O2 consumed, we need to know the molar mass of O2. The molar mass of O2 is 32.00 g/mol.

# Define the variables
m_o2 = 32.00  # molar mass of O2 in g/mol
n_mgo = 0.050  # number of moles of MgO produced

n_o2 = (2 * n_mgo) / 1  # since 2 moles of MgO produce 1 mole of O2

print(f"The number of moles of O2 consumed is {n_o2} mol")

The number of moles of O2 consumed is 0.100 mol. Since the result has only three significant figures, we can round it to 0.100 mol.

Conclusion

In this article, we have explored the rules for significant figures and applied them to a balanced chemical reaction. We have performed calculations to determine the mass of MgO produced, the number of moles of MgO produced, and the number of moles of O2 consumed. By following the rules for significant figures, we have ensured that our calculations are accurate and precise.

References

CRC Handbook of Chemistry and Physics. 97th ed. Boca Raton, FL: CRC Press, 2016.
NIST Chemistry WebBook. National Institute of Standards and Technology, 2020.

Glossary

Significant figures: The number of digits in a measurement that are known to be reliable.
Molar mass: The mass of one mole of a substance.
Moles: A unit of measurement for the amount of a substance.
Grams: A unit of measurement for mass.

=====================================================================================

Q: What are significant figures?

A: Significant figures are the digits in a measurement that are known to be reliable. They are used to express the accuracy and precision of a measurement.

Q: How do I determine the number of significant figures in a measurement?

A: To determine the number of significant figures in a measurement, look for the following:

Non-zero numbers: All non-zero numbers have at least one significant figure.
Zeros between non-zero numbers: Zeros between non-zero numbers are significant.
Zeros at the end of a number: Zeros at the end of a number are significant only if the number contains a decimal point.
Zeros at the beginning of a number: Zeros at the beginning of a number are not significant.

Q: What is the difference between accuracy and precision?

A: Accuracy refers to how close a measurement is to the true value. Precision refers to how consistent a measurement is.

Q: How do I round a number to the correct number of significant figures?

A: To round a number to the correct number of significant figures, follow these steps:

Determine the number of significant figures: Determine the number of significant figures in the measurement.
Look at the first non-significant digit: Look at the first non-significant digit (the digit after the last significant digit).
Round up or down: If the first non-significant digit is 5 or greater, round up. If it is less than 5, round down.

Q: What is the rule for significant figures when adding or subtracting numbers?

A: When adding or subtracting numbers, the result should have the same number of decimal places as the number with the fewest decimal places.

Q: What is the rule for significant figures when multiplying or dividing numbers?

A: When multiplying or dividing numbers, the result should have the same number of significant figures as the number with the fewest significant figures.

Q: How do I handle zeros in a measurement?

A: Zeros in a measurement can be significant or non-significant, depending on the context. If the number contains a decimal point, zeros at the end of the number are significant. If the number does not contain a decimal point, zeros at the end of the number are not significant.

Q: What is the importance of significant figures in chemical calculations?

A: Significant figures are essential in chemical calculations because they help us determine the accuracy and precision of our measurements and calculations. By following the rules for significant figures, we can ensure that our calculations are accurate and precise.

Q: How do I apply significant figures to a balanced chemical reaction?

A: To apply significant figures to a balanced chemical reaction, follow these steps:

Determine the number of significant figures: Determine the number of significant figures in each measurement.
Perform the calculation: Perform the calculation using the correct number of significant figures.
Round the result: Round the result to the correct number of significant figures.

Q: What are some common mistakes to avoid when working with significant figures?

A: Some common mistakes to avoid when working with significant figures include:

Rounding too many times: Rounding too many times can lead to inaccurate results.
Not following the rules for significant figures: Not following the rules for significant figures can lead to inaccurate results.
Not considering the context: Not considering the context of the measurement can lead to inaccurate results.

Q: How do I determine the number of significant figures in a calculated value?

A: To determine the number of significant figures in a calculated value, follow these steps:

Determine the number of significant figures in each measurement: Determine the number of significant figures in each measurement.
Perform the calculation: Perform the calculation using the correct number of significant figures.
Round the result: Round the result to the correct number of significant figures.

Q: What is the difference between a calculated value and a measured value?

A: A calculated value is a value that is obtained by performing a calculation using measured values. A measured value is a value that is obtained by measuring a quantity.

Q: How do I apply significant figures to a calculated value?

A: To apply significant figures to a calculated value, follow these steps:

Determine the number of significant figures in each measurement: Determine the number of significant figures in each measurement.
Perform the calculation: Perform the calculation using the correct number of significant figures.
Round the result: Round the result to the correct number of significant figures.

Q: What are some common applications of significant figures in chemistry?

A: Some common applications of significant figures in chemistry include:

Calculating the number of moles of a substance: Calculating the number of moles of a substance requires the use of significant figures.
Determining the concentration of a solution: Determining the concentration of a solution requires the use of significant figures.
Calculating the volume of a substance: Calculating the volume of a substance requires the use of significant figures.

Q: How do I determine the number of significant figures in a volume measurement?

A: To determine the number of significant figures in a volume measurement, follow these steps:

Determine the number of significant figures in the length and width: Determine the number of significant figures in the length and width of the container.
Determine the number of significant figures in the height: Determine the number of significant figures in the height of the container.
Calculate the volume: Calculate the volume using the correct number of significant figures.

Q: What is the rule for significant figures when converting between units?

A: When converting between units, the result should have the same number of significant figures as the number with the fewest significant figures.

Q: How do I apply significant figures to a conversion between units?

A: To apply significant figures to a conversion between units, follow these steps:

Determine the number of significant figures in each measurement: Determine the number of significant figures in each measurement.
Perform the conversion: Perform the conversion using the correct number of significant figures.
Round the result: Round the result to the correct number of significant figures.

Q: What are some common mistakes to avoid when working with significant figures in conversions between units?

A: Some common mistakes to avoid when working with significant figures in conversions between units include:

Not following the rules for significant figures: Not following the rules for significant figures can lead to inaccurate results.
Not considering the context: Not considering the context of the measurement can lead to inaccurate results.
Not rounding the result correctly: Not rounding the result correctly can lead to inaccurate results.

Q: How do I determine the number of significant figures in a calculated value that involves a conversion between units?

A: To determine the number of significant figures in a calculated value that involves a conversion between units, follow these steps:

Determine the number of significant figures in each measurement: Determine the number of significant figures in each measurement.
Perform the conversion: Perform the conversion using the correct number of significant figures.
Round the result: Round the result to the correct number of significant figures.

Q: What is the difference between a calculated value and a measured value in a conversion between units?

A: A calculated value is a value that is obtained by performing a calculation using measured values. A measured value is a value that is obtained by measuring a quantity.

Q: How do I apply significant figures to a calculated value that involves a conversion between units?

A: To apply significant figures to a calculated value that involves a conversion between units, follow these steps:

Determine the number of significant figures in each measurement: Determine the number of significant figures in each measurement.
Perform the conversion: Perform the conversion using the correct number of significant figures.
Round the result: Round the result to the correct number of significant figures.

Q: What are some common applications of significant figures in chemistry that involve conversions between units?

A: Some common applications of significant figures in chemistry that involve conversions between units include:

Calculating the number of moles of a substance: Calculating the number of moles of a substance requires the use of significant figures and conversions between units.
Determining the concentration of a solution: Determining the concentration of a solution requires the use of significant figures and conversions between units.
Calculating the volume of a substance: Calculating the volume of a substance requires the use of significant figures and conversions between units.

Q: How do I determine the number of significant figures in a calculated value that involves a conversion between units and a calculation?

A: To determine the number of significant figures in a calculated value that involves a conversion between units and a calculation, follow these steps:

Determine the number of significant figures in each measurement: Determine the number of significant figures in each measurement.
Perform the conversion: Perform the conversion using the correct number of significant figures