Q: A student measures the mass of a beaker using the electronic balance shown and records 31.8116 g. If the true mass is 31.8000 g, calculate the percent error using the formula $$\text{Percent Error} = \frac{\text{Experimental Value} - \text{True Value}}{\text{True Value}} \times 100.$$

$$\text{Percent Error} = \frac{31.8116 - 31.8000}{31.8000} \times 100 = 0.0365\%$$

Q: A student uses the electronic balance to measure the mass of a sample three times and obtains: 31.8116 g, 31.8118 g, and 31.8117 g. Calculate the mean mass using $$\text{Mean} = \frac{\sum_{i=1}^{n} x_i}{n}.$$

$$\text{Mean} = \frac{31.8116 + 31.8118 + 31.8117}{3} = 31.8117\text{ g}$$

Q: A student measures the mass of a beaker as 31.8116 g, then adds water and measures the mass as 35.8116 g. If the volume of water added is 4.00 ml, what is the calculated density of water using $$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$$?

$$\text{Density} = \frac{35.8116 - 31.8116}{4.00} = 1.00\text{ g/ml}$$

Q: A student measures the mass of a sample using the electronic balance and records 31.8116 g, 31.8117 g, and 31.8118 g. Calculate the standard deviation using $$\text{S.D.} = \sqrt{\frac{\sum_{i=1}^{n} (x_i - x)^2$}{n-1}}$$ where $$x is $$the mean.

$$\text{S.D.} = \sqrt{\frac{(31.8116-31.8117)^2$ + (31.8117-31.8117)^2$ + (31.8118-31.8117)^2$}{2}} = 0.0001\text{ g}$$

Question 1

Which laboratory instrument is shown in the image, and what is its primary function?

Accepted Answer

Electronic balance; used to measure the mass of substances.

Question 2

If the electronic balance in the image displays a reading of 31.8116 g, what is the uncertainty associated with this measurement?

Accepted Answer

±0.0001 g (uncertainty is in the last digit displayed)

Question 3

A student measures the mass of a beaker using the electronic balance shown and records 31.8116 g. If the true mass is 31.8000 g, calculate the percent error using the formula $$	ext{Percent Error} = \frac{	ext{Experimental Value} - 	ext{True Value}}{	ext{True Value}} 	imes 100.$$

Accepted Answer

$$	ext{Percent Error} = \frac{31.8116 - 31.8000}{31.8000} 	imes 100 = 0.0365\%$$

Question 4

Why is it important to record all digits displayed by the electronic balance, as shown in the image?

Accepted Answer

Because the uncertainty is in the last digit displayed, and all digits contribute to the precision of the measurement.

Question 5

A student uses the electronic balance to measure the mass of a sample three times and obtains: 31.8116 g, 31.8118 g, and 31.8117 g. Calculate the mean mass using $$	ext{Mean} = \frac{\sum_{i=1}^{n} x_i}{n}.$$

Accepted Answer

$$	ext{Mean} = \frac{31.8116 + 31.8118 + 31.8117}{3} = 31.8117	ext{ g}$$

Question 6

Which of the following best describes the precision of the electronic balance shown in the image?

Accepted Answer

It can measure mass to the nearest 0.0001 g.

Question 7

If a student repeatedly measures the mass of the same object using the electronic balance and gets values that are very close to each other but not close to the true value, which term best describes these measurements?

Accepted Answer

Precise but not accurate

Question 8

What type of error is most likely minimized by using the electronic balance shown in the image, assuming proper calibration and handling?

Accepted Answer

Systematic error

Question 9

A student measures the mass of a beaker as 31.8116 g, then adds water and measures the mass as 35.8116 g. If the volume of water added is 4.00 ml, what is the calculated density of water using $$	ext{Density} = \frac{	ext{Mass}}{	ext{Volume}}$$?

Accepted Answer

$$	ext{Density} = \frac{35.8116 - 31.8116}{4.00} = 1.00	ext{ g/ml}$$

Question 10

If the electronic balance is not calibrated correctly, which type of error will most likely affect the measurements?

Accepted Answer

Systematic error

Question 11

Why is the uncertainty in the mass measurement from the electronic balance assumed to be in the last digit displayed?

Accepted Answer

Because the instrument's precision is defined by the smallest increment it can display.

Question 12

A student measures the mass of a sample using the electronic balance and records 31.8116 g, 31.8117 g, and 31.8118 g. Calculate the standard deviation using $$	ext{S.D.} = \sqrt{\frac{\sum_{i=1}^{n} (x_i - x)^2$}{n-1}}$$ where $$x is $$the mean.

Accepted Answer

$$	ext{S.D.} = \sqrt{\frac{(31.8116-31.8117)^2$ + (31.8117-31.8117)^2$ + (31.8118-31.8117)^2$}{2}} = 0.0001	ext{ g}$$

Measurements, Accuracy, Precision, and Density Determination in the Chemistry Laboratory

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