A Chemist Needs To Know The Mass Of A Sample Of $MgCl_2$ To 2 Significant Digits. She Puts The Sample On A Digital Scale And It Reads:$\[ \begin{tabular}{l|l|l|l} \hline 0 & 0 & 2 & 65 \, \text{g} \\ \end{tabular} \\]Is This
Introduction
In the world of chemistry, precision and accuracy are crucial when working with samples. A chemist's ability to determine the mass of a sample with precision is essential for various experiments and calculations. In this article, we will explore the scenario of a chemist who needs to know the mass of a sample of magnesium chloride ($MgCl_2$) to 2 significant digits. We will examine the digital scale reading and determine if it meets the required precision.
The Digital Scale Reading
The digital scale reads: ${ \begin{tabular}{l|l|l|l} \hline 0 & 0 & 2 & 65 , \text{g} \ \end{tabular} }$
Understanding Significant Figures
Significant figures are a way to express the precision of a measurement. In this case, the chemist needs to know the mass of the sample to 2 significant digits. This means that the measurement should have at least 2 digits that are certain, with the third digit being uncertain.
Analyzing the Digital Scale Reading
Let's analyze the digital scale reading: ${ \begin{tabular}{l|l|l|l} \hline 0 & 0 & 2 & 65 , \text{g} \ \end{tabular} }$
The first digit is 0, which is uncertain because it is a leading zero. The second digit is also 0, which is uncertain for the same reason. The third digit is 2, which is certain. The fourth digit is 6, which is certain. The fifth digit is 5, which is uncertain.
Determining the Precision of the Measurement
Based on the analysis, the measurement has 3 certain digits (2, 6, and 5) and 2 uncertain digits (0 and 0). This means that the measurement has a precision of 3 significant digits.
Conclusion
In conclusion, the digital scale reading of 265 g has a precision of 3 significant digits, which is more than the required precision of 2 significant digits. Therefore, the chemist can be confident that the mass of the sample of $MgCl_2$ is 265 g to 2 significant digits.
Significance of the Measurement
The precision of the measurement is crucial in chemistry because it affects the accuracy of calculations and experiments. In this case, the chemist needs to know the mass of the sample to 2 significant digits to ensure that the experiment is conducted accurately.
Limitations of the Measurement
One limitation of the measurement is that it has a precision of 3 significant digits, which is more than the required precision. This means that the measurement is more precise than necessary, which can be a limitation in certain situations.
Future Directions
In the future, the chemist may need to determine the mass of a sample with even greater precision. In this case, the chemist may need to use a more precise instrument, such as a balance or a spectrometer.
Conclusion
In conclusion, the digital scale reading of 265 g has a precision of 3 significant digits, which is more than the required precision of 2 significant digits. The chemist can be confident that the mass of the sample of $MgCl_2$ is 265 g to 2 significant digits. The precision of the measurement is crucial in chemistry, and the chemist should be aware of the limitations of the measurement.
References
- [1] "Significant Figures." Chemistry LibreTexts, Libretexts, 2020.
- [2] "Digital Scales." ScienceDirect, Elsevier, 2020.
Appendix
The following is a list of the significant figures in the measurement:
- 2 (certain)
- 6 (certain)
- 5 (uncertain)
- 0 (uncertain)
- 0 (uncertain)
The following is a list of the uncertain digits in the measurement:
- 0 (leading zero)
- 0 (second digit)
- 5 (third digit)
The following is a list of the certain digits in the measurement:
- 2 (third digit)
- 6 (fourth digit)
- 5 (fifth digit)
A Chemist's Dilemma: Determining the Mass of a Sample with Precision ====================================================================
Q&A: Understanding the Precision of a Measurement
Q: What is the significance of significant figures in chemistry? A: Significant figures are a way to express the precision of a measurement. In chemistry, they are crucial in calculations and experiments to ensure accuracy.
Q: How do you determine the number of significant figures in a measurement? A: To determine the number of significant figures in a measurement, you need to look for the certain digits. The certain digits are the digits that are known to be accurate. The uncertain digits are the digits that are not known to be accurate.
Q: What is the difference between a certain digit and an uncertain digit? A: A certain digit is a digit that is known to be accurate, while an uncertain digit is a digit that is not known to be accurate. In the measurement 265 g, the digits 2, 6, and 5 are certain, while the digits 0 are uncertain.
Q: How do you handle leading zeros in a measurement? A: Leading zeros are zeros that appear at the beginning of a measurement. They are not considered significant figures because they do not add any information to the measurement. In the measurement 265 g, the leading zeros are not considered significant figures.
Q: What is the importance of precision in chemistry? A: Precision is crucial in chemistry because it affects the accuracy of calculations and experiments. In chemistry, precision is used to determine the amount of a substance, the concentration of a solution, and the rate of a reaction.
Q: How do you determine the precision of a measurement? A: To determine the precision of a measurement, you need to look at the number of significant figures. The more significant figures a measurement has, the more precise it is.
Q: What is the difference between precision and accuracy? A: Precision refers to the consistency of a measurement, while accuracy refers to how close a measurement is to the true value. In chemistry, precision is used to determine the amount of a substance, while accuracy is used to determine the true value of a measurement.
Q: How do you handle measurements with multiple significant figures? A: When a measurement has multiple significant figures, you need to consider all of the significant figures when making calculations. In the measurement 265 g, the significant figures are 2, 6, and 5.
Q: What is the importance of significant figures in calculations? A: Significant figures are crucial in calculations because they affect the accuracy of the results. In chemistry, significant figures are used to determine the amount of a substance, the concentration of a solution, and the rate of a reaction.
Q: How do you round a measurement to a certain number of significant figures? A: To round a measurement to a certain number of significant figures, you need to look at the digit to the right of the significant figure. If the digit is 5 or greater, you round up. If the digit is less than 5, you round down.
Q: What is the difference between rounding up and rounding down? A: Rounding up means increasing the significant figure by 1, while rounding down means decreasing the significant figure by 1. In the measurement 265 g, rounding up would result in 270 g, while rounding down would result in 260 g.
Q: How do you handle measurements with decimal places? A: When a measurement has decimal places, you need to consider the decimal places when making calculations. In the measurement 2.65 g, the decimal places are 2 and 5.
Q: What is the importance of decimal places in chemistry? A: Decimal places are crucial in chemistry because they affect the accuracy of the results. In chemistry, decimal places are used to determine the amount of a substance, the concentration of a solution, and the rate of a reaction.
Conclusion
In conclusion, significant figures are crucial in chemistry because they affect the accuracy of calculations and experiments. Understanding the precision of a measurement is essential in chemistry, and it requires knowledge of significant figures, decimal places, and rounding. By following the rules of significant figures, chemists can ensure that their measurements are accurate and reliable.