Answer to Question #173676 in General Chemistry for Uhan

Question

3. Two students determine the percentage of lead in a sample as a laboratory exercise. The true percentage is 22.52%. The students’ results for three determinations are as follows:

1. 22.52, 22.28, 22.74 (Student A)

2. 22.64, 22.58, 22.62 (Student B)

If precision can be judged by examining the standard deviations from the average value for that data set. The lower the deviation, the more precise the measurement is. Which student has the most precise data set? What is the standard deviation?

A. 0.03, student B

B. 0.03, Student A

C. 0.02, Student B

D. 0.02, Student A

4. Use the given choices below to describe the set of data collected. Data is determined to be accurate if the % error is ≤ 5.00% and precise if the SD ≤ 0.10.

Volume measurements of water contained in a 108 g/cm3 box: 109, 108, 107

A. precise only

B. accurate only

C. neither accurate nor precise

d. both accurate and precise.

Answer 1

3.

For student A

1. Average value =$\frac{22.52+22.28+ 22.74 }{3}=22.51$

error in value

$\Delta x_1=|22.52-22.51|=.01$

$\Delta x_2=|22.28-22.51|=0.23$

$\Delta x_3=|22.74-22.51|=0.23$

relative error= .01+.23+.23/3=0.16

For student B

average value = 22.64 + 22.58 + 22.62/3=22.61

$\Delta x_1=|22.64-22.61|=.03$

$\Delta x_2=|22.58-22.61|=.03$

$\Delta x31=|22.62-22.61|=.01$

relative error= 0.03+0.03+0.01/3=0.023

So, most precise data is for 0.02. Student B

4.

There are three data

for volume contained in 108 g/cm3 box:

x₁=109,

x₂=108,

x₃=107

Average value= $109+108+107/3=108$

$\Delta x_1=|109-108|=1$

$\Delta x_2=|108-108|=0$

$\Delta x_3=|107-108|=1$

SD=$1+0+1/3=0.667$

error= $\frac{0.667}{108}\times 100=0.617$ %

since error is less than 5%

so it is accurate option (B) accurate