A researcher explores the ideal gas equation. He measures the pressure of a system at different temperatures ( keeping the volume and moles of the gas constant) and creates a plot of P versus T. What is the slope of the line that results if the volume is 1.0L when 1.0 mol of gas is used in the exploration?
The slope will be nRT. You will have to use the ideal gas law to derive this.
Thank you but I am not sure what you mean by derive it
I am still very confused
Slope intercept form is y=mx+b. The gas law is PV=nRT. The graph is a plot of P vs. T, so we will isolate P on one side of the equal sign and let that be Y and 1/V is our x, since plotting P vs 1/V is the only way to obtain a straight line.
Rearrange, P=nRT/V + 0 is our equation, and since 1/V is our x, then m is equal to nRT our slope. What I did was derive the equation of the line.
I apologize. Everything that I told you was correct except for the X axis. The X axis is T not V, so starting to where I misstated, slope intercept form is y=mx+b. The gas law is PV=nRT. The graph is a plot of P vs. T, so we will isolate P on one side of the equal sign and let that be Y and T is our x, since plotting P vs T obtains a straight line, rearranging causes the equation of the line to be P=(nR/V)T+ b, where the slope is equal to nR/V, P =Y, and T=X. Once again I apologize, it was late when I was looking at this and it was early when I replied.
To find the slope of the line on a P versus T plot, we need to use the ideal gas equation:
PV = nRT
Where:
P = pressure
V = volume
n = moles of gas
R = ideal gas constant
T = temperature
In this case, the volume (V) and moles of gas (n) are constant, as mentioned. Therefore, we can rewrite the equation as:
P = (nR/V) * T
Now, since the volume is 1.0L and 1.0 mol of gas is used, we can substitute these values into the equation:
P = (1.0 mol * R / 1.0 L) * T
The value of R is a constant, which is 0.0821 L•atm/(mol•K).
Therefore:
P = (0.0821 mol•atm/ K) * T
Now we can see that the equation is in the form y = mx, where P is the dependent variable (y), and T is the independent variable (x). The slope of this line (m) will be equal to the coefficient of T in the equation.
So, the slope of the line is 0.0821 mol•atm/K.