Question #d4c35
1 Answer
Explanation:
The idea here is that when the pressure and the temperature of a gas are kept constant, the volume of the gas and the number of moles present in the sample have a direct relationship described by Avogadro's Law.
In other words, under these conditions, when you increase the number of moles of gas present in the sample, the volume will increase as well. Similarly, when you decrease the number of moles of gas present in the sample, the volume will decrease as well.
http://www.chegg.com/homework-help/questions-and-answers/avogadro-s-law-states-volume-v-gas-directly-related-number-moles-n-gas-temperature-pressur-q12216065
Mathematically, you can write this as
V_1/n_1 = V_2/n_2V1n1=V2n2
Here
V_1V1 ,n_1n1 represent the volume and the number of moles of gas at an initial stateV_2V2 ,n_2n2 represent the volume and the number of moles of gas at a final state
Now, the first thing that you need to do here is to figure out how many moles of helium are present in the cylinder when the volume of the gas is equal to
Rearrange the equation to solve for
n_2 = V_2/V_1 * n_1n2=V2V1⋅n1
As you know, helium has a molar mass of
n_1 = (2.00 color(red)(cancel(color(black)("g"))))/(4.0026color(red)(cancel(color(black)("g"))) "mol"^(-1)) = "0.4997 moles"
You can thus say that you have
n_2 = (2.70 color(red)(cancel(color(black)("L"))))/(2.00color(red)(cancel(color(black)("L")))) * "0.4997 moles"
n_2 = "0.6746 moles"
This means that the number of moles of helium increased by
Deltan = n_2 - n_1
Deltan = "0.6746 moles " - " 0.4997 moles"
Deltan = "0.1749 moles"
To convert this to grams, use the molar mass of helium
0.1749 color(red)(cancel(color(black)("moles He"))) * "4.0026 g"/(1color(red)(cancel(color(black)("mole He")))) = color(darkgreen)(ul(color(black)("0.700 g")))
I'll leave the answer rounded to three sig figs.