How many moles of gas does it take to occupy 150 liters at a pressure of 4.0 atm and a temperature of 200k? Can you explain to me how to get the answer please?

Question

jfraser · Answer

have you heard of the ideal gas law? It combines pressure, volume, temperature, and moles into one big equation

anonymous · Answer

i have not. i have a medical problem and am always in the hospital and dont have time to really get in depth with what im studying but im really trying to understand this problem can you please help me

ipwnbunnies · Answer

$$PV = nRT$$
This is the Ideal Gas Equation JFraser is referring to. It can describe many relationships of different properties of a gas.

Anyway. You are given 4 of these values: P for pressure, V for volume, T for temperature, and R is the gas constant. The gas constant is something that never changes.

anonymous · Answer

is the gas constant 0.0821?

ipwnbunnies · Answer

Numerically, yes. But the units of this version are important.
$$R = 0.0821 \frac{L*atm}{mol*K}$$

anonymous · Answer

my chemistry teacher doesnt want to give me extra time even thought ive been recently diagnosed with a pituitary tumor. i really appreciate this. my teacher wants the answer in 20 minutes.

anonymous · Answer

so 150x4.0/molx200??

anonymous · Answer

what would the mole be

jfraser · Answer

moles is what you're looking to find

anonymous · Answer

how would i find it?

jfraser · Answer

before plugging in values, it's usually more helpful to rearrange the equation into a form so that the unknown is what you're solving for

jfraser · Answer

The ideal gas law usually looks like this:

$$P*V = n*R*T$$

jfraser · Answer

without plugging in numbers, can you rearrange that equation so you get something that looks like: $$n = ??$$

anonymous · Answer

n= p * v *r *t??

ciarán95 · Answer

The Ideal Gas Law models the relationship between the pressure, volume, temperature and the number of moles of what we refer to as an ideal gas. You may not of heard of this term before, but an ideal gas is like a 'perfect' gas which we can model and identify under certain assumptions. These links should help fill you in on a bit more info if you need it: http://www.chemguide.co.uk/physical/kt/idealgases.html http://www.sparknotes.com/chemistry/gases/ideal/summary.html These list out the assumptions or the 'rules' which we use to judge whether a certain gas is ideal or not ideal, which in the case of the latter it is just a real gas. The main points of difference between the two are that the gas molecules must essentially be far apart and exert no intermolecular forces on each other, if the gas is to be ideal. With any gas, we often find that with higher temperatures and lower pressures, the gas leans towards becoming more ideal than real. So, to solve this problem we must assume that the gas in question is indeed ideal and then we can apply the Ideal Gas Law: $$PV = nRT$$ where: - P is the pressure in Pascals - V is the volume in m^3 (metres cubed) - n is the number of moles of the gas we have - T is the temperature of the gas in degrees Kelvin - R is a constant in this equation, known as the Universal Gas Constant, which has a value of 8.31 J/mol.K - We know that the gas is at a pressure of 4 atm, or 4 times atmospheric pressure. To convert this figure to Pascals we use the fact that: $$1 atm = 1 \times 10^{5}Pa$$ approximately. So, 4 atm will convert to (4)(1 x 10^5 Pa), or simply 4 x 10^5 Pa - We also know that the volume of the gas is 150 litres. Like before, to convert this value into m^3 we use the conversion factor: $$1 L = 1 \times 10^{-3}m ^{3}$$ So, 150 liters will convert to (150)(1 x 10^-3 m^3), or 0.15 m^3 when you work it out. - Finally, we know that the temperature of the gas is 200 degrees Kelvin. As this is already in the correct unit for the Ideal Gas Law to hold, we don't need to change it. If we rearrange the equation from above to get 'n', or the number of moles, on its own, we get: $$n = \frac{ PV }{ RT }$$ So, given that we know P, V and T in the correct units, and R is a constant of 8.31 J/mol.K, we can substitute in the values: $$n = \frac{ (4 x 10^{5}Pa)(0.15m ^{3)} }{ (8.31 J mol ^{-1}K ^{-1})(200K) }$$ and this, when you work it out, should give you the answer to the number of moles you have. Hope that helps you! :)

anonymous · Answer

where did you get the j from?

anonymous · Answer

wouldnt it be 4*150/0.0821*200= n?

jfraser · Answer

there are so many ways of measuring pressure and volume, without the proper UNITS, this is very difficult. According to your data, your numbers are correct. You have to be sure that you're dividing by (R*T), not just R, then multiplying by T

$$n = \frac{P*V}{R*T}$$

anonymous · Answer

so when i plug this in , n will be the answer for the question?

jfraser · Answer

yep

anonymous · Answer

im sorry can you tell me what R is again? is r 0.0821?

jfraser · Answer

for these units, the value of R is $ 0.0821\frac{L*atm}{mol*K}$

when you do out the algebra, every unit in R will cancel except for the moles, which is what you're looking for

anonymous · Answer

i dont really get that. so when plugged in it should be 4*150/0.0821*200

anonymous · Answer

my teacher will call me any second for the answer and i want to make sure i get it right

anonymous · Answer

will the answer to the question be 36.54? thats what i got

jfraser · Answer

that's what i get, GJ

anonymous · Answer

so it is the answer?

jfraser · Answer

it is

anonymous · Answer

yaaaay thank you i really appreciate it your time

jfraser · Answer

YW