A sample of O2 gas is placed in a sealed 1.00 L flask and pressure is measured as temperature is changed. The data are plotted and the slope of the resulting line is equal to 0.00400 atm/K. The line passes through the origin of the graph. There are (blank) g of O2 gas in the flask. (R = 0.08206 L*atm/K*mol)

Check this out. Check my thinking.

P1/T1 = P2/T2 OR
P/T = k so the slope of 0.004 must be k.
We can rearrange the ideal gas law to
PV = nRT, rearrange to
PV/T = nR; therefore,
PV/T = k = nR (since V = 1 liter)
Therefore, 0.004 = nR.
You know R, calculate n = number of mols.
From mols you can determine grams O2.
Check my thinking.

To find the number of grams of O2 gas in the flask, we need to use the ideal gas law equation:

PV = nRT

Where:
P = pressure of the gas (in atm)
V = volume of the flask (in liters)
n = number of moles of the gas
R = ideal gas constant (0.08206 L*atm/K*mol)
T = temperature of the gas (in Kelvin)

In the given problem, the slope of the resulting line on the graph is equal to 0.00400 atm/K. The line passes through the origin, which means that when the temperature is zero, the pressure is zero. This implies that the initial pressure (P) of the gas is zero.

We can rewrite the ideal gas law equation as:

P = (nRT) / V

Substituting the given values:

0.00400 atm/K = (n * 0.08206 L*atm/K*mol * T) / 1.00 L

Now we can solve for the number of moles (n) of the gas:

n = (0.00400 atm/K * 1.00 L) / (0.08206 L*atm/K*mol * T)

Since we're looking for the number of grams, we need to convert moles to grams using the molar mass of O2, which is 32 g/mol. Thus, the equation becomes:

n (in moles) = (0.00400 atm/K * 1.00 L) / (0.08206 L*atm/K*mol * T)
n (in grams) = n (in moles) * molar mass of O2

Finally, we substitute the value of n (in moles) into the equation, and we need to know the temperature (T) to find the number of grams of O2 gas in the flask.