Measurement

Measurements A measurement is not complete unless it has a unit. A unit is the part of the measurement that tells us what scale or standard is being used to represent the results of the measurement. The need for common units applies to scientists, who measure quantities such as mass, length, time, and temperature.

The Metric System There are two measurement systems that are commonly used: 1.The English System (used in the United States) 2.The Metric System (used in most of the rest of the world) In Chemistry, we will use the metric system. This system has long been preferred for most scientific work.

SI Units The International System (or le Systeme Internationale in French) is the type of units that are based on the metric system. These units are also known as SI units. We will be using SI units in Chemistry. SI Units PropertyUnitSymbol masskilogramkg length/distancemeterm timeseconds temperatureKelvinK amount of a substance molemol

Metric Prefixes The fundamental SI units are not always a convenient size, so the SI system uses prefixes to change the size of the unit. Metric prefixes SymbolValue Scientific Notation mega-M1,000, kilo-k1, deci-d centi-c milli-m micro-µ nano-n

Measuring Length Length is measured with a ruler or meter stick On a 12” ruler, there are 30.5cm On a meter stick, there are 100cm The SI unit is the meter, abbreviated “m”

Measuring Volume Volume is the amount of three-dimensional space occupied by a substance. The SI unit of volume is the cubic meter, abbreviated “m 3,” but in Chemistry we will use liters, abbreviated “L” or the milliliter, abbreviated “mL” Volume is measured with a graduated cylinder

Volume and the meniscus… Measuring volume with a graduated cylinder is complicated by a meniscus. A meniscus is the curvature of the surface of the water. Water “sticks” to the walls of the graduated cylinder, but only on the sides and not the middle. When you look at the surface, the water level is not straight. Measurement should be at the lowest point. You must read the meniscus at eye level in order to get an accurate reading. You should place the graduated cylinder on the table and then lower your head to be able to read the meniscus at eye level.

Measuring Mass The SI unit is the kilogram, abbreviated “kg,” but in Chemistry we will use grams, abbreviated “g” Mass is measured with a balance

Measuring Temperature The SI unit is the Kelvin, but in Chemistry we will use degrees Celsius, abbreviated, “°C” Temperature is measured with a thermometer

Uncertainty in Measurement A measurement always has some degree of uncertainty. Whenever a measurement is made with a ruler, graduated cylinder, or thermometer, an estimate is required.

Uncertainty with a ruler On the ruler to the right, you can accurately measure the pencil length to 8.2cm, but it is not exactly on the line. So, an estimation of the next division is required. This estimation is your degree of uncertainty. One student might say 8.24cm, another might say 8.25cm, a third might say 8.23cm. To account for the uncertainty, the measurement usually is written 8.24 ± 0.01 cm. The “± 0.01 cm” tells us that the measurement is uncertain to 1/100 of a centimeter.

Uncertainty with a thermometer The same is true for thermometers: On the thermometer to the right, you can accurately measure the temperature to be 23°C, but it is not exactly on the line. So an estimation of the next division is required. This estimation is your degree of uncertainty. To account for the uncertainty, the measurement should be 23.5 ± 0.1 °C. This tells us that the thermometer is uncertain to 1/10 of a degree.

Uncertainty with a graduated cylinder The same is true for graduated cylinders: On the graduated cylinder to the right, you can accurately measure the temperature to be 43mL, but it is not exactly on the line. So an estimation of the next division is required. This estimation is your degree of uncertainty. To account for the uncertainty, the measurement should be 43.1 ± 0.1 mL. This tells This tells us that the graduated cylinder is uncertain to 1/10 of a mL.

Experimental Error

In the laboratory, NO measurement is exact. There are always errors that affect our results – whether we are using a 10-cent ruler or an $800 balance.

Accuracy & Precision Accuracy measures how close a measured value is to the true value or accepted value. Precision measures how closely two or more measurements agree with each other. Precision is sometimes referred to as “repeatability” or “reproducibility.” A measurement which is highly reproducible tends to give values which are very close to each other.

Sources of Experimental Error When conducting an experiment, there are three types of errors that you will encounter: “human” error, random error, and systematic error.

A human error is simply another word for mistake, blunder, or screw-up. Examples include: Not setting up an experiment correctly Misreading an instrument Using the wrong chemical(s) Not following directions Spilling or general sloppiness Bad calculations, doing math incorrectly, using the wrong formula Human errors are NOT a source of experimental error, but rather they are “experimenter’s” error. Human Error

Random Error Random errors are unavoidable variations that will either increase or decrease a given measurement. Examples may include: Fluctuations in the laboratory balance (your sample may weigh a few hundredths of a gram higher or lower at any given time, depending on the quality of the balance and the conditions in the room). Using a stopwatch to time a reaction (regardless of how careful you are you will sometimes stop the watch too soon and sometimes too late). To minimize random errors, try to use high-quality laboratory equipment whenever possible and use consistent techniques when performing an experiment. Since random errors are equally likely to be high as low, performing several trials (and averaging the results) will also reduce their effect considerably.

Systematic Error Systematic error is an error inherent in the experimental setup which causes the results to be skewed in the same direction every time. For example: A mis-calibrated thermometer may increase all temperature readings by 0.5°C. A cloth tape measure used to measure the length of an object could be stretched out from years of use (as a result, all of your length measurements would be too small). Substituting grams of rock salt for grams of table salt in an experiment will affect the rate at which the reaction takes place. In this case, the reaction rate would decrease due to the decreased surface area. Since systematic errors always skew data in one direction, they cannot be eliminated by averaging. However, they can usually be avoided by changing the way in which the experiment was carried out (using more reliable equipment, modifying a procedure, changing laboratory conditions, etc.).

Analyzing Experimental Error The most common way to analyze experimental error is to compare your results with a known value (if available) using the percent error formula: