(a) Calculate the mass of nitrogen present in a volume of...

(a) Calculate the mass of nitrogen present in a volume of 3000 cm$^3$ if the gas is at 22.0$^\circ$C and the absolute pressure of 2.00$\times$ 10${^-}{^1}{^3}$ atm is a partial vacuum easily obtained in laboratories. (b) What is the density (in kg/m$^3$) of the N$_2$ ?

Transcript

00:01 So in this question is given that the nitrogen is present in a volume of 3000 cm cube so let me convert this into si system that is meter cube so to convert this cm cube into meter cube we multiply that by 10 to the power minus 6 so this is the volume of nitrogen present and it says that the temperature of the gas is at 22 degrees celsius so 22 degrees celsius needs to be converted into kelvin how by adding 273 that makes it in kelvin and which is equal to 2 .95 kelvin so this is the temperature of the nitrogen gas says that the absolute pressure of the gas is 2 times 10 to the power minus 13 atm so again to convert this into as i we need to to get we need to multiply a 1b multiply this into this by 1 .01 into 10 to the power 5 then that will give me this pressure in pascal now what else is given okay nothing else is given so we need to calculate the mass of nitrogen present so to calculate that we use the ideal gas equation that says that b is equal to an rd where p is the pressure v is the volume n is the number of moles r is the universal gas constant whose value is given as r is equal to 8 .314 in si and the unit is through normal for kelvin so and we need to calculate mass so what we do is instead of number of moles we write mass upon molecular weight where m is mass and capital m is molecular weight of molecular weight so the gas that we have used here is nitrogen and that is that has a molecular weight of 28 so that is nearly equal to for molecular weight of adjunct nearly equal to 28 so that is 28 grams per mole that can be written as 28 into 10 to the power minus 3 kg per more okay so we add this as it is so we are keen in determining the mass of nitrogen.

03:03 So small m is equal to p m b by r t.

03:12 Now we know the value of p we know the value of m, we know the value of m, we know the value of p, we know the value of r, we know the value of t.

03:21 So in all these values in here, you get mass to be 6 .9 into 10 to the power, minus 16 cases.

03:33 This is how you determine the mass of the nitrogen in the given, in the given time...

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