A container of volume 19.4 cm3 is initially filled with air. The container is then evacuated at 0oC to a pressure of 6.0 mPa. How many molecules are in the container after evacuation if we assume that air is an ideal gas?
Since the gas is ideal, we can use the Ideal Gas Law:
PV = nRT
where
P = pressure in atm
V = volume in L
n = number of moles of air
R = universal gas constant = 0.0821 L-atm/mol-K
T = temperature in K
We first convert the given in the appropriate units:
V = 19.4 cm^3
cm^3 is also equal to mL. Thus there are 1000 cm^3 for every 1 L, or
V = 19.4 / 1000 = 0.0194 L
P = 6 mPa
The conversion is: 101325 Pa = 1 atm, thus
P = (6 / 1000) / 101325 =
T = 0 C
We just add 273 to make it Kelvin:
T = 0 + 273 = 273 K
Substituting to the equation:
PV = nRT
n = PV/RT
n = (5.92 10^-8)(0.0194) / (0.0821)(273)
n = 5.125 * 10^-11 moles
Note that this is only the moles. To get the number of molecules, note that 1 mol = 6.022 * 10^23 representative particles. Thus,
5.125 * 10^-11 * 5.125 * 10^-11
= 3.087 * 10^13 molecules
Check the significant figures.
Hope this helps :3
*lol sorry, in the last calculation that should be
5.125 * 10^-11 * 6.022 * 10^23
but the answer is still the same. :)
To find the number of molecules in the container, we need to use the ideal gas law equation, which relates the pressure, volume, and temperature of an ideal gas.
The ideal gas law equation is: PV = nRT
Where:
P = pressure (in pascals, Pa)
V = volume (in cubic meters, m^3)
n = number of moles of gas
R = ideal gas constant = 8.314 J/(mol·K)
T = temperature (in Kelvin, K)
First, we need to convert the given values to the appropriate units. The volume is given in cm^3, which needs to be converted to m^3, and the pressure is given in mPa, which needs to be converted to Pa.
1 cm^3 = 1 × 10^(-6) m^3 (since 1 m = 100 cm, then 1 m^3 = (100 cm)^3 = 1 × 10^6 cm^3)
1 mPa = 1 × 10^(-3) Pa (since 1 Pa = 1 N/m^2 and 1 mN = 1 × 10^(-3) N)
So, the volume of the container is 19.4 × 10^(-6) m^3, and the pressure is 6.0 × 10^(-6) Pa.
Next, we need to convert the temperature given in degrees Celsius to Kelvin. The conversion is:
T(K) = T(°C) + 273.15
Since the temperature is given as 0°C, the temperature in Kelvin is 0 + 273.15 = 273.15K.
Now, we can use the ideal gas law equation to find the number of moles of gas (n). Rearranging the equation, we have:
n = PV / RT
Substituting the given values, we get:
n = (6.0 × 10^(-6) Pa) × (19.4 × 10^(-6) m^3) / (8.314 J/(mol·K) × 273.15K)
Calculating this expression will give us the number of moles of gas in the container.
Lastly, to find the number of molecules, we can use Avogadro's number, which states that there are 6.022 × 10^23 molecules in one mole of a substance.
Number of molecules = n × Avogadro's number
By plugging in the value of n we obtained and multiplying it by Avogadro's number, we can find the final answer to the question.