A cylinder with a movable piston contains 2.00 of helium, , at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the volume was changed from 2.00 to 4.30 ? (The temperature was held constant.)
A cylinder with a movable piston contains 2.00g of helium, , at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the volume was changed from 2.00L to 4.30L ? (The temperature was held constant.)
I would use PV = nRT first. You know V, n, R, and T, so you can determine p.
Second part of the problem says p stays constant. Use PV = nRT again. Here you know the old p (since it stays constant), the new V, along with R and T. Calculate new n and grams He from that.
T doesn't change; just make up a convenient T. I would make it something easy like 300 K.
To solve this problem, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
In this case, the pressure is held constant, so we can rewrite the equation as V1/n1 = V2/n2, where V1 and V2 are the initial and final volumes, and n1 and n2 are the initial and final number of moles.
From the information given, the initial volume is 2.00 L and the final volume is 4.30 L.
We also know that the initial number of moles of helium is 2.00 mol because we have 2.00 grams of helium at room temperature, and helium has a molar mass of 4.00 g/mol.
Now, we can rearrange our equation to solve for n2 (the final number of moles):
V1/n1 = V2/n2
n2 = n1 * (V2/V1)
n2 = 2.00 mol * (4.30 L/2.00 L)
n2 = 4.30 mol
To find the number of grams of helium that were added, we can subtract the initial number of moles from the final number of moles:
n_added = n2 - n1
n_added = 4.30 mol - 2.00 mol
n_added = 2.30 mol
Finally, we can calculate the mass of the added helium using its molar mass:
mass_added = n_added * molar mass
mass_added = 2.30 mol * 4.00 g/mol
mass_added = 9.20 g
Therefore, 9.20 grams of helium were added to the cylinder.