This table shows experimental data for gas volume and...

This table shows experimental data for gas volume and pressure. TABLE CANNOT COPY a. Show that $P=k(1 / V)$ for each trial. Remember to add 14.7 $\mathrm{lb} / \mathrm{in}^{2}$ to the values in the last column to account for atmospheric pressure. b. Show that $P V=k$ for each trial. c. Create a graph of $P$ versus $V$ . What does the graph tell you about the relationship between gas pressure and volume? d. Create a graph of $P$ versus 1$/ V$ . What does the graph tell you about the relationship between gas pressure and inverse volume? e. Use the graphs from parts $c$ and $d$ to estimate the volume when the pressure is 30 $\mathrm{lb} / \mathrm{in}^{2}$ . f. Use the graphs from parts $c$ and d to estimate the pressure when the volume is 50 $\mathrm{mL} .$

This table shows experimental data for gas volume and pressure.
TABLE CANNOT COPY
a. Show that $P=k(1 / V)$ for each trial. Remember to add 14.7 $\mathrm{lb} / \mathrm{in}^{2}$ to the values in the last column to account for atmospheric pressure.
b. Show that $P V=k$ for each trial.
c. Create a graph of $P$ versus $V$ . What does the graph tell you about the relationship between gas pressure and volume?
d. Create a graph of $P$ versus 1$/ V$ . What does the graph tell you about the relationship between gas pressure and inverse volume?
e. Use the graphs from parts $c$ and $d$ to estimate the volume when the pressure is 30 $\mathrm{lb} / \mathrm{in}^{2}$ .
f. Use the graphs from parts $c$ and d to estimate the pressure when the volume is 50 $\mathrm{mL} .$

Key Concepts

Boyle's Law

Boyle's Law states that for a given amount of gas at a constant temperature, the pressure of the gas is inversely proportional to its volume. This relationship is often written as PV = k, where k is a constant. The law shows that if the volume increases, the pressure decreases proportionally, and vice versa, assuming no change in temperature or amount of gas.

Inverse Proportionality

Inverse proportionality is a relationship between two variables in which one variable increases as the other decreases. In this context, pressure (P) is inversely proportional to volume (V), meaning that doubling the volume would result in halving the pressure if the amount of gas and temperature remain constant. This concept is central to understanding the behavior of gases under changing volumes.

Proportionality Constant

The constant of proportionality, denoted as k in the equation PV = k, represents the product of pressure and volume at a given state of the gas. This constant is crucial because it encapsulates the condition that, for a fixed amount of gas at a constant temperature, the product of the pressure and volume remains unchanged regardless of how one variable changes relative to the other.

Atmospheric Pressure Correction

Atmospheric pressure correction involves adding the standard atmospheric pressure to the measured pressure values when the provided data represents gauge pressure rather than absolute pressure. This adjustment ensures that calculations and graphs reflect the absolute pressure experienced by the gas, which is essential for applying Boyle's Law accurately.

Graphical Data Analysis

Graphical data analysis in this context involves plotting the relationship between pressure (P) and volume (V), and between pressure (P) and the inverse of volume (1/V), to visually interpret the behavior of the gas. The P versus V graph typically shows a hyperbolic curve indicative of inverse proportionality, while the P versus 1/V graph yields a linear relationship which confirms the mathematical model of P = k(1/V). Estimations from these graphs allow for the prediction of values such as volume at a given pressure and vice versa.

Transcript

00:01 This is question 7 from chapter 11, section 3, and it's a big problem on the relationship between pressure and volume.

00:11 So in your textbook, they give you this chart, and there's a column of pressure, and then there's a column of volume.

00:22 So we are going to find the, we're going to use boyle's law to solve for these.

00:28 So boils law is pv is equal to k so in row one we have 60 milliliters and 10 pounds as 10 pounds per square inch as the pressure so i'm going to do 60 times 10 and this is going to come out to be 600 in row 2 the volume is 40 and the pressure is 15 so 40 times 15 is also 600 row three we have 30 for volume and we have 20 for pressure this also comes out to 600 and row four and row five actually also come out to 600 for they're given pressure and volume so after all five trials these are all constant with 600 so it is proven that pressure times volume is equal to k or the constant.

01:37 So now we are going to graph pv is equal to k.

01:42 So first i want to draw my graph.

01:47 So we have volume and milliliters.

01:53 And we're going to have pressure on the sides and with that pounds per square inch.

02:00 So pv is equal to k is actually an inverse relationship so we are actually going to draw a line like this so as you can tell when the volume is increasing pressure is decreasing okay so now we are going to draw another graft when instead of having the volumes and millers we have the inverse of volume so we're going to have one over v in the x -axis in no liters and i'm going to have the pressure on the y so pounds inches squared okay so this one is different we know that p v equal to k is an inverse relationship but now we have the inverse of volume so when you have the inverse of volume it actually makes it a direct relationship to pressure because they're no longer an inverse relationship.

03:10 So this is actually going to be drawn as a straight line when you have the inverse of volume...

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