Balances true mass

If mass m is read from a balance, the true mass m of the object weighed in vacuum is given by10... 

Solution Assuming that the balance weights have a density of 8.0 g/mL and the density of air is 0.001 2 g/mL, we find the true mass by using Equation 2-1 ... 

Figure 2-5 shows buoyancy corrections for several substances. When you weigh water with a density of 1.00 g/mL, the true mass is 1.001 I g when the balance reads 1.000 0 g. The... 

SO2 uptake was measured at total system pressures in the range of 20 to 50 Torr, consisting of 17.5 Torr H2O vapor with the balance either helium or argon. The observed mass accommodation coefficients, 74, are plotted in Figure 2 as a function of the inverse of the calculated diffusion coefficient of SO2 in each H20-He and l O-Ar mixture. The diffusion coefficients are calculated as a sum of the diffusion coefficients of SO in each component. The diffusion coefficients for SO in He and in Ar are estimated from the diffusion coefficient of SO2 in H 0 (Dg p = 0.124 (101) by multiplying this value by the quantity (mH-/mH Q)V2, anti (mAr/m 2o) 2> respectively. The curves in Figure 2 are plots ofEquation 7 with three assumed values for 7 0.08,0.11 and 0.14. The best fit to the experimental values of is provided by 7 = 0.11. Since gas uptake could be further limited by liquid phase phenomena as discussed in the following section, 7502 = 0.11 is a lower limit to the true mass accommodation coefficient for SO2 on water. 

There are only two occasions where measured weight equals true mass, when k = 1. This occasion occurs when measurements are made in a vacuum or the density of a sample is equal to the density of the mass standard. Fortunately, the greatest differences only occur when an object s density is particularly low (0.1% for density 1.0 g/cm3 and about 0.3% for density = 0.4 g/cm3). In most situations, the effect of air buoyancy is significantly smaller than the tolerance of the analytical balance. The effects of varying densities (of objects being weighed) and varying air densities are shown in Table 2.22. 

One approach to avoiding the problem of air buoyancy is to weigh an object in a vacuum (known as weight in vacuo ). Such readings provide an object s true mass as opposed to its apparent mass. There are a variety of vacuum balances made precisely for this purpose. However, vacuum balances are expensive, require expensive peripheral equipment (such as vacuum systems), and are neither fast nor efficient to use. 

The true mass of the wire is 2.000 g. Therefore, Student B s results are more precise than those of Student A (1.972 g and 1.968 g deviate less from 1.970 g than 1.964 g and 1.978 g from 1.971 g), but neither set of results is very accurate. Student C s results are not only the most precise, but also the most accurate, since the average value is closest to the true value. Highly accurate measurements are usually precise too. On the other hand, highly precise measurements do not necessarily guarantee accurate results. For example, an improperly calibrated meter stick or a faulty balance may give precise readings that are in error. 

The true mass of a glass bead is 0.1026 g. A student takes four measurements of the mass of the bead on an analytical balance and obtains the following results 0.1021 g, 0.1025 g, 0.1019 g, and 0.1023 g. Calculate the mean, the average deviation, the standard deviation, the percentage relative standard deviation, the absolute error of the mean, and the relative error of the mean. 

A simple example of a systematic error is provided by a balance. Balances are often set to read a mass of zero before being used to weigh a sample. Suppose a speck of dust falls upon the pan of a balance after zeroing. This will cause the indicated mass of any object to be greater than the true mass. For example, if the speck has a mass of 0.0001 g, all objects will have an apparent mass which is 0.0001 g too high. 

Mass by weighing on a balance with unequal arms n. If Wj is the value for one side, W2 the value for the other, the true mass,... 

Of course the preceding thought-experiment, in which calibration of the balance is conducted in a vacuum, is an unrealistic example of the buoyancy effect. Consider now a realistic case where the calibration of the balance and the weighing of the nnknown object are both conducted at atmospheric pressure now the variation arises because the densities (and thus the volumes) of the standard mass and the unknown are different. The buoyancy force on the steel standard is stiU the same (equivalent to the gravitational force on 1.5 x 10 g), but in this case this buoyancy force is accounted for in the calibration procedure. Assume that the object to be weighed is a powdered or liquid chemical with density 1 g.cm and also of true mass 10.0000g, so its volume is lO.Ocm the mass of air that it displaces is thus 12 x 10 g. In other words, the upward (buoyancy) force on the sample is greater than that on the steel standard used to calibrate the balance by an amount equivalent to a mass of (12 — 1.5 = 10.5) X 10 g, and the indicated mass on... 

Another minor source of bias arises when the balance is calibrated at one location and is then used at another location of significantly different elevation, i.e., at a different distance from the centre of the Earth. Then the gravitational force on the object in the weighing pan will vary according to the inverse-square law. Suppose the calibration was done at sea level (radius of the Earth approxi-mately6.37x lO m), but is then used at a location 1000m above sea level. Then the indicated reading R ai for an object of true mass will be ... 

The measurements chemists make are often used in calculations to obtain other related quantities. Different instruments enable us to measure a substance s properties The meter stick measures length or scale the buret, the pipet, the graduated cylinder, and the volumetric flask measure volume the balance measures mass and the thermometer measures temperature. Any measured quantity should always be written as a number with an appropriate unit. To say that the distance between New York and San Francisco by car along a certain route is 5166 is meaningless. We must specify that the distance is 5166 kilometers. The same is true in chemistry units are essential to stating measurements correctly. 

The electronic signal-processing part of a balance is comparable to a digital voltmeter, except that the display is calibrated in units of mass. The accuracy (correspondence between a displayed value and the true mass on the balance) of a modern professional-grade balance is ensured by auto-... 

To ensure that S eas is determined accurately, we calibrate the equipment or instrument used to obtain the signal. Balances are calibrated using standard weights. When necessary, we can also correct for the buoyancy of air. Volumetric glassware can be calibrated by measuring the mass of water contained or delivered and using the density of water to calculate the true volume. Most instruments have calibration standards suggested by the manufacturer. 

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