The Following Table Shows the Relationship Between Pressure (In Atmospheres)

question 238

Essay

The following table shows the relationship between pressure (in atmospheres) and volume (in liters) of hydrogen gas at 0 °C. $$\begin{array} { | l | c | c | c | c | c | c | } \hline \text { Pressure (atm) } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Volume (L) } & 22.4 & 11.2 & 7.5 & 5.6 & 4.5 & 3.7 \\\hline\end{array}$$ (a) Find the average rate of change of volume with respect to pressure for the following pressure intervals:
(i) [1, 3]
(ii) [2, 3]
(iii) [4, 5]
(b) Plot the data points and fit an appropriate power function to these data.(c) Use the model from part (b) and determine the instantaneous rate of change of volume with respect to pressure.(d) Compare the instantaneous rate at P = 5 with the average rate for [4, 5]. Which is larger? Why is this the case?

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Definitions:

Salivary Gland

Exocrine glands located in the mouth that produce saliva, aiding in digestion and oral hygiene.

Canine

A tooth located between the incisors and premolars, pointed in shape and used for tearing food.

Premolar

A type of tooth located between the canine teeth and molars in the mouth, used for crushing and grinding food.

Incisor

A front tooth specialized in cutting food, found in both the upper and lower jaws of mammals.