A sample of helium behaves as an ideal gas as it is heated at constant pressure from 273 K to 373 K. If 15.0 J of work is done by the gas during this process, what is the mass of helium present?
I am not sure what equations to use for this problem....
PV=nRT
p dV + V dp = n R dT
p is constant here so
p dV = n R dT
work = integral p dV = nR dT
p(V2-V1) = n R (T2-T1)
so 15 = n R (T2-T1)
doesnt that give me an answer in moles? ...is there a way to convert moles to mg?
so i got the answer to be .01804 moles
and i know one mole of helium is 4.03 g
do i just multiply the two together? and then divide by 10000 to convert g to mg?
never mind. I made a silly error.
i got .01804 moles...multiplied that times 4.03grams and then multiplied that times 1000 and got 72.7mg.
got it! thanks so much!
what are we solving for in this equation?? 15 = n R (T2-T1)
we know n, we know R, we know t1 and t2...so what do we solve for?
To solve this problem, we need to use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas (which is constant in this case)
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
Since the pressure is constant and the helium is behaving as an ideal gas, we can simplify the equation to:
V = (nRT) / P
Now let's consider the work done by the gas. Work is defined as the change in energy, which can be expressed as work = -PΔV (where ΔV is the change in volume).
In this case, the work done by the gas (W) is 15.0 J, and since the pressure is constant, the equation becomes:
W = -PΔV
Since the gas is being heated at constant pressure, the change in volume (ΔV) can be expressed as:
ΔV = Vf - Vi
Now we can substitute the equation for work into the equation for change in volume:
15.0 J = -P(Vf - Vi)
Since the pressure is constant, we can rearrange the equation:
Vf - Vi = -15.0 J / P
Now, let's substitute the equation for volume into the ideal gas law equation:
(nRTf / P) - (nRTi / P) = -15.0 J / P
We can cancel out the pressure (P) on both sides of the equation:
nRTf - nRTi = -15.0 J
Let's rearrange the equation to solve for n:
n(RTf - RTi) = -15.0 J
n = -15.0 J / (RTf - RTi)
Now we have an equation for the number of moles (n) of helium present. To find the mass, we need to know the molar mass of helium. The molar mass of helium is approximately 4.003 g/mol.
Let's calculate the mass:
Mass of helium = n * molar mass
Note: We need to convert the number of moles (n) to grams.
Mass of helium = (n * molar mass) g
I hope this explanation helps you solve the problem and understand the steps involved.