Measurement and Uncertainty Lab Manual

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Barstow Community College *

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Chemistry

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Jan 9, 2024

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Measurement and Uncertainty Lab Manual Resources: https://www.youtube.com/watch?app=desktop&v=-zuIftmI-6I https://www.youtube.com/watch?v=H3vYS6cBtpQ https://www.youtube.com/watch?v=ae4NMm763mM Overview In this investigation, students will use basic scientific measuring equipment to determine the accuracy and uncertainty associated with measurements using common laboratory glassware. Time Requirements Needed but not supplied: • Permanent marker Overview Video: Measurement and Uncertainty Outcomes • Determine the uncertainty of measurements with standard glassware and equipment. • Determine the accuracy of measurements with standard glassware. Why Should I Care Communication is paramount in the scientific community because reproducibility is what establishes the theories and laws we recognize within the various scientific disciplines. If presented theories cannot be reproduced by scientists across the globe, they will not be confirmed. And scientists cannot reproduce an experiment if the conditions, procedures, and results are not clearly communicated via terminology every scientist understands. The General Conference on Weights and Measures began creating a common language among scientists when they defined the International System of Units, abbreviated SI (from the French Le Systeme International d'Unites). You can consider the SI system as the modern form of the metric system. The SI system is the only system of measurement that is officially recognized in nearly every country in the world.

When reporting measurements, significant figures complement the SI units by allowing scientists to recognize how precise a reported answer is, or how much uncertainty there is within reported results. This also allows scientists to immediately gauge whether their equipment is capable of accurately reproducing the reported values of an experiment. Background Measurements can come in many forms, such as length, weight (mass), volume and temperature, but there are many other forms you may encounter in the future. This investigation will focus on two: how to measure weight and volume, and some common equipment used to measure both. Using Your Scale To measure the weight of an object (more scientifically referred to as the mass) a scale or balance is used. Your lab kit contains a small scale that will be used to weigh all substances in your course. Within the box your scale arrives in are two AAA batteries and the balance with a lid. When you remove the lid, there are complete instructions on the use of the scale on the inside. When looking at the top of the scale, there are 5 points of interest. First is the pan, this is the large, flat surface above the LCD screen. Objects you wish to weigh are placed on the pan. Below the pan is the LCD screen. This is where the mass of an object on the pan will be displayed. Below the screen are three buttons reading, from left to right, ON/OFF, MODE, and TARE. When you first turn on the balance by pressing the ON/OFF button the screen should read 0.00 g (g stands for grams in this instance). This indicates there is no mass on the balance. If the letter at the end is not g, you can press the MODE button until “g” is listed as the units. If the screen is not indicating a mass of 0.00, you can press the TARE button to re-zero the scale. After you press the TARE button, the scale should reset to 0.00 g. The scale has a maximum capacity of 100 g; if a mass greater than 100 g is placed on the pan, the screen will read “0_Ld,” indicating too large a mass has been placed on the pan. Measuring Liquids To measure a volume of liquid, typically a piece of glassware, such as a beaker or graduated cylinder, is used. The equipment is placed on a flat countertop or table, and liquid is poured into it. The bottom of the meniscus (the concave layer or water at the top) is where the volume is measured against the scale (Figure 1). As you will see in Activity 2, the volume you read from a particular piece of glassware may be at best an estimate. Having measurable results is an integral part of the scientific method. Scientists must contend with two main factors while taking measurements: the accuracy of the measurement and the precision of the measurement. Accuracy is how close a set of data is to the actual value. 'Accuracy is gauged by comparing the measured value of a known standard to its true value'.Ignore color of text. Precision refers to how close a data point is to other measurements in a data set Measuring Liquids (cont... ) A data set that is accurate is not necessarily precise, whereas a very precise data set could be highly inaccurate. Forces that affect the accuracy and precision in measurements are error. In scientific settings, error is defined as the difference between the measured value and the actual value, where the actual value is a known value, sometimes referred to as a standard. Two main types of error exist: systematic and random. Systematic error is a type of error that causes measurements to be inaccurate by a certain value in a particular direction. Systematic error can be further divided into absolute and relative error. Absolute error has both magnitude and direction and is represented as a discrete value. For example, if your alarm clock is slow by five minutes it has a systematic, absolute error. Each morning you will be getting up five minutes later than planned and dealing with the potential repercussions. Absolute error can be calculated as follows:

absolute error = |measurement - actual value| absolute error = |6:35 - 6:40| = 5 minutes The || brackets indicate that you take the absolute value of a calculation. An absolute value means the value in the bracket will always be positive. There is a second type of systematic error called relative error , or percent error, which is expressed as a percentage. One of the more common measuring devices with built-in percent error is the speedometer of a car. Most automobile manufacturers have a tolerance of ±2% in their speedometers. Measuring Liquids (cont... ) This means that any given speedometer could read between 2% too slow or 2% too fast. If your speedometer reads 61 mph, while actually traveling 60 mph, the percent error is calculated using the equation below. relative error = ((|measurement - actual value| / actual value )) x 100% relative error = ((|61 mph - 60 mph|/ 60 mph)) x 100% = 1.6% Related to relative error is the concept of percent error. Percent error is calculated by comparing a measurement against an accepted value. Typically an accepted value is measured with a high level of precision and accuracy, but it is still a measured value—no matter what, there is always some form of error associated with a measured value. percent error = ((|measurement - accepted value|/ accepted value)) x 100% An important characteristic of systematic error, both absolute and relative, is that it can be either corrected or accounted for in future measurements as it has both direction and magnitude. With your alarm clock, you could change the time so that it is no longer 5 minutes fast; with the speedometer you could mathematically correct for the relative error in future readings. Although systematic error can be corrected for if discovered, random error will be present in all measurements. Through improved experimental design and best lab practices, random error can be reduced but it can never be eliminated. The most common form of random error in a lab setting comes from the equipment. This type of random error is most commonly referred to as uncertainty. Uncertainty is the limit of quantifiable measurement with confidence using measuring equipment. Measuring Liquids (cont... ) One method for determining the uncertainty of an analog measuring device is to utilize the scale provided on the equipment. For example, on the 10-mL graduated cylinder Figure 1, there are graduations (lines) every 0.1 mL. In Figure 1, the bottom of the meniscus is between the graduations of 6.7 and 6.8. Most people would read the volume as 6.75 mL. You can say with certainty that the water is between 6.70 and 6.80 mL, but many people would have difficulty determining a finer range of certainty. A simple method for determining the measured value and the uncertainty is as follows: measured value = high interval + low interval 2 6.75 = 6.80 + 6.70 2 Uncertainty = high interval - low interval 2 0.05 = 6.80 - 6.70 2 The measured value in this example would be 6.75 mL ± 0.05 mL. The ±0.05 mL indicates confidence that the actual value for this measurement is between 6.80 mL and 6.70 mL. With a digital device, such as the balance supplied in your equipment kit, uncertainty is generally limited to the last significant figure. For example, a balance that can read to tenths of a gram would have an uncertainty in the tenth’s

place, typically of ±0.1 or ±0.2 grams. Uncertainty is generally calculated using a standard and a high number of measurements. A standard is a chemical or piece of equipment that has a known quantity associated with it, in this case a mass. For this activity, plastic cups are used as your standard for determining the uncertainty in your balance. Error, uncertainty, and equipment segue into the mathematical concept of significant figures. Significant figures are digits relating to the precision of measurement. There are some general rules for determining if a digit is significant: Measuring Liquids (cont... ) • All non-zero digits are considered significant. • Zeros appearing anywhere between two non-zero digits are significant (0.1003 has 4 significant figures). • Leading zeros are not significant (0.0076 has 2 significant figures). • Trailing zeros in a number containing a decimal point are significant. For example, 35.000 has five significant figures. Uncertainty limits the precision and the number of significant figures in a measurement. In the example above, the 6.75 mL of water in the graduated cylinder has three significant figures. The 6 before the decimal and the 7 and 5 after the decimal are all considered significant. This is confirmed with the uncertainty of 0.05 mL. In this instance the uncertainty indicates that there are no additional significant figures beyond the hundredths place. However, if the graduated cylinder was measured at 6.75, but the uncertainty was determined to be 0.20 mL. The number of significant figures would be limited to two, and the measurement would be reported as 6.8 mL ± 0.2 mL. In the next example, let’s assume that the volume measurement above had a relative error of 1%. 6.75mL x 1% 100% = 0.0675mL This would equate to an absolute error of .0675 mL in the measurement. Like 6.75 mL, .0675 mL has three significant figures. However, the process of multiplication and division has added a false precision to the result. 6.75 mL ± 0.0675 mL is incorrect because the calculated error has additional precision that the original measurement can contain. In this instance the proper measured value would be written as 6.75 mL ± 0.07 mL. In general, you cannot gain significant figures and you cannot gain precision in a measurement through mathematical functions. Knowledge Check Question 2 What is one way to reduce uncertainty when using analog measuring equipment? Never use glass equipment. There is no way to reduce uncertainty. Right Answer,

Use the scale provided on the equipment. If only two numbers are reported on a scale, estimate what the next three numbers would be. Guess at whatever number you want. Submit Feedback If the bottom of the meniscus is between the graduations of 6.7 and 6.8. Most people would read the volume as 6.75 mL. You can say with certainty, based on the scale, that the water is between 6.70 and 6.80 mL, but many people would have difficulty determining a finer range of certainty. Experimental Design Materials Select each tab to continue Needed from the equipment kit Needed but not supplied Scale Graduated cylinder, 10 mL

Graduated cylinder, 50 mL Erlenmeyer flask, 25 mL Beaker, 250 mL 2 Plastic cups Thermometer Needed but not supplied • Permanent marker Safety Safety goggles should be worn during this investigation. There are no additional safety concerns. Read all the instructions for this laboratory activity before beginning. Follow the instructions closely and observe established laboratory safety practices, including the use of appropriate personal protective equipment (PPE) described in the Safety and Procedure section. Do not eat, drink, or chew gum while performing this activity. Wash your hands with soap and water before and after performing the activity. Clean up the work area with soap and water after completing the investigation. Keep pets and children away from lab materials and equipment. Pre-Lab Assessment Introduction Directions: Complete this pre-lab assessment to continue to the rest of the investigation. You will need a score of 100% to pass the assessment. This assessment can be attempted as many times as necessary to achieve a passing score. You may return to the pre-lab sections to study before each attempt.For each question, select your response and then click Submit to see how you did. Click Next to continue to the next question. A final results page will appear upon completion of this assessment with your overall performance. Start Question 1 How many significant figures are in the number 0.08546000? 5

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