(a) An ideal gas occupies a volume of 1.6-cm3 at 20°C and atmospheric pressure. Determine the number of molecules of gas in the container.
(b) If the pressure of the 1.6-cm3 volume is reduced to 1.6 10-11 Pa (an extremely good vacuum) while the temperature remains constant, how many moles of gas remain in the container?
ok, i took the equation PV = nRT
where
P = atmospheric pressure which i believe is 1.5 x 10 ^5
V = 1.6 x 10 ^-6 m^3
R = 8.31
and T = 293
and then i mulitiplied the answer i got times 6.02 x 23 to convert to molecules....but it's not right.
I would memorize atmospheric pressure as 101.3kPa
so i did that and I got 4.0 X 10 ^16
and it's still wrong...am I just missing a conversion somewhere or something like that?
never mind, i got it. thanks so much!
To solve these problems, you need to use the ideal gas equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Let's go through each question step by step:
(a) To determine the number of molecules of gas in the container, we first need to calculate the number of moles of gas using the ideal gas equation.
Given:
P = atmospheric pressure = 1.5 x 10^5 Pa
V = 1.6 cm^3 = 1.6 x 10^-6 m^3
R = 8.31 J/(mol·K)
T = 20°C = 20 + 273 = 293 K
Now, plug in the values into the ideal gas equation:
(1.5 x 10^5) * (1.6 x 10^-6) = n * (8.31) * (293)
Simplifying the equation, you get:
n = [(1.5 x 10^5) * (1.6 x 10^-6)] / [(8.31) * (293)]
Performing the calculation, you will find the value of n, which represents the number of moles of gas in the container.
Once you have the number of moles, you can convert it to the number of molecules by multiplying it by Avogadro's number, 6.02 x 10^23, since one mole contains that many molecules.
(b) For this question, you need to use the same ideal gas equation:
Given:
P = 1.6 x 10^-11 Pa
V = 1.6 x 10^-6 m^3
R = 8.31 J/(mol·K)
T = constant (so no need to calculate again)
Now, apply the ideal gas equation:
(1.6 x 10^-11) * (1.6 x 10^-6) = n * (8.31) * (T)
Simplifying the equation, we have:
n = [(1.6 x 10^-11) * (1.6 x 10^-6)] / [(8.31) * (T)]
Since T is constant, you can solve for n using the given values.
Once you find the number of moles, you can leave it in that form. There's no need to convert it to the number of molecules in this case because it's not required for the question.
Remember to double-check your calculations to ensure accuracy.