08/28/2020Determination of Densities of Solids and LiquidsPurposeThis activity will teach you about measurements, their accuracy, precision, and uncertainty andhow each of these can be stated. You will learn techniques for measuring solids and liquids in thelaboratory, and you will learn how to evaluate the quality of a balance. Then you will use theseskills to determine the density of a solid.BackgroundMany experiments involve the measurement of mass, volume, or length. No matter how carefullyyou make a measurement, no matter how carefully you read the measuring instruments, therewill always be some uncertainty in every measured value. This uncertainty can be minimized butnever completely eliminated. The quality of a set of measurements is stated in terms of accuracyand precision.A.Accuracy of a MeasurementTheaccuracyof a measured value concerns the agreement of that value with the “true” value, orwith what is generally accepted as the “true” value. Relative error is frequently stated as percenterror.¿experimental value – truevalue∨¿true valuex100%%error=¿The United States National Institute for Standards and Technology (NIST) provides samples ofknown “true value” for technical and scientific use.B.Precision of Measured ValuesPrecisionis a measure of the agreement between two or more measurements that are averaged togive the reported value (each measurement being made under the same conditions). Whileaccuracy is a measure of agreement between a reported value and the true value, precisionreflects the agreement between the individual measurements, such as the values used to obtainthe average. Errors that affect precision occur randomly and have an equal probability of beingon the high side or the low side of the average of a set of measurements. A set of measuredvalues can be of high precision and high accuracy, or of low precision and low accuracy, or ofany other high-low combination.Page1of12

08/28/2020Figure 1. Example of Accuracy and PrecisionThe most common method used to express the precision in a set of measured values is thestandard deviation, a statistical measure of the scatter of data about the average, or mean, of aset of measurements.The smaller the standard deviation, the higher the precision of the set ofmeasurements. Standard deviation (s.d.) is defined by the following equation:s.d. =√∑(Xi−Xmean)2N−1Xi= value of one measurementXmean= mean (average) of all N measurementsN = number of measurements in the data setC.Balances – Measuring MassThe Single Pan Automatic BalanceA typical student-grade automatic balance is shown in Figure 2. The mass of the object beingweighed is displayed in digital format in a window on the front of the balance. The balance isautomatically zeroed when it is turned on (of course, the pan must be empty). An automaticbalance can be capable of accuracy to the second, third, or fourth place after the decimal. Nomatter which balance you use, always observe the following precautions:1.The balance must be level, vibration-free, and kept in its place.

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