Question

1. different sample amounts of the same liquid were obtained. the mass and volume of each sample was measured. the results were plotted according the graph below. what is the density of the liquid? a. 2.0x10^6g/ml b. 6.7x10^ - 1g/ml c. 5.0x10^ - 1g/ml d. 3.0x10^6g/ml 5. a student measures the length of an object using a centimeter ruler. assume the object begins at zero centimeters and ends where the arrow is shown below. what is the length of the object in centimeters; what is its length when converted to meters? a. 16.6cm; 1.66m b. 16.60cm; 0.1660m c. 16.60cm; 1.660m d. 16.6cm; 0.166m 6. a series of changes have been made to the atomic model over the last 200 years. as a result, the current accepted atomic model is drastically different from the original atomic model.

Explanation:

Step1: Recall density formula

Density $
ho=\frac{m}{V}$, where $m$ is mass and $V$ is volume. From the graph, we can take two - point values. Let's take the points $(0,1)$ and $(9,5)$. The change in mass $\Delta m = 5 - 1=4$ g and the change in volume $\Delta V=9 - 0 = 9$ mL.

Step2: Calculate density

$
ho=\frac{\Delta m}{\Delta V}=\frac{4}{9}\approx0.44$ g/mL. Another way is to use the slope - intercept form of a line $y = mx + b$. Here $y$ is mass $m$, $x$ is volume $V$, and the slope $m$ is the density. The line passes through $(0,1)$ and $(9,5)$. The slope $m=\frac{5 - 1}{9-0}=\frac{4}{9}\approx0.44$ g/mL. Among the given options, the closest one is B. $6.7\times10^{-1}$ g/mL.

For the length measurement:

Step1: Read length from ruler

The ruler is marked in centimeters. The arrow is between 16 cm and 17 cm, and it appears to be at the 6 - th small division (assuming each centimeter is divided into 10 small divisions). So the length in centimeters is $16.6$ cm.

Step2: Convert to meters

We know that $1$ m = $100$ cm. So to convert from centimeters to meters, we divide by 100. $16.6$ cm=$\frac{16.6}{100}=0.166$ m.

Answer:

1. B. $6.7\times10^{-1}$ g/mL
2. B. $16.60$ cm; $0.1660$ m