How to derive the ideal gas equation -Equation for ideal gas (PV=nRT) - PV =nRT derivation - Kisembo

in this lecture, i get to show you PV = nRT derivation. - How to derive the ideal gas equation. I would like to thank all of you that keep sending financial support via   / kisemboacademy   your continued support has enabled us to keep producing these videos. Keep the support coming through and may God bless you more. This video shows how to derive PV=nRT transcript; 0:00:00.030,0:00:04.740 let we may all know the ideal gas is a 0:00:02.190,0:00:08.670 hypothetical or call it a theoretical 0:00:04.740,0:00:10.380 does with preset conditions however this 0:00:08.670,0:00:12.389 hypothetical ideal gas is a good 0:00:10.380,0:00:15.269 approximation of how many gases tend to 0:00:12.389,0:00:17.340 behave in today's session we explore how 0:00:15.269,0:00:21.060 to derive the ideal gas equation or call 0:00:17.340,0:00:24.230 it the general gas equation coming up 0:00:21.060,0:00:26.670 [Music] 0:00:24.230,0:00:28.529 now of course we all know that there are 0:00:26.670,0:00:31.320 three gas laws and right before us we 0:00:28.529,0:00:32.940 have an expression for Boyle's law we 0:00:31.320,0:00:34.800 definitely come up with the ideal gas 0:00:32.940,0:00:36.739 equation for from the three gaseous 0:00:34.800,0:00:38.969 close the Boyle's law the pressure law 0:00:36.739,0:00:41.690 Chelsea's law now Boyle's law like 0:00:38.969,0:00:44.160 Evalia stated in previous sessions 0:00:41.690,0:00:46.920 pressure is inversely proportional to 0:00:44.160,0:00:49.079 volume and this is how the expression is 0:00:46.920,0:00:51.270 that PV is equal to a constant that is 0:00:49.079,0:00:52.920 the expression for Boyle's law then we 0:00:51.270,0:00:55.110 have the expression for the pressure law 0:00:52.920,0:00:56.879 that pressure is directly proportional 0:00:55.110,0:00:59.670 to the temperature and this is how it 0:00:56.879,0:01:02.070 comes to conclude that P over T it gives 0:00:59.670,0:01:04.170 us a constant K this is our second 0:01:02.070,0:01:08.760 equation then we have our third equation 0:01:04.170,0:01:10.049 that velocity that volume of a gas is 0:01:08.760,0:01:13.049 there to proportional to the absolute 0:01:10.049,0:01:16.710 temperature and V of R T is going to 0:01:13.049,0:01:18.240 give us K this is Charles's law and this 0:01:16.710,0:01:20.549 is our third expression so we are going 0:01:18.240,0:01:22.439 to get these three expressions and we're 0:01:20.549,0:01:25.200 going to multiply them all when we 0:01:22.439,0:01:27.420 multiply all of them then we shall end 0:01:25.200,0:01:29.850 up with the ideal gas equation and this 0:01:27.420,0:01:33.390 is how we do it what the position was PV 0:01:29.850,0:01:36.060 is equal to K so we get PV over K is 0:01:33.390,0:01:37.829 going to be equal to K of course we're 0:01:36.060,0:01:39.450 going to multiply this by the second 0:01:37.829,0:01:41.400 equation so we get our second equation 0:01:39.450,0:01:43.409 that's our second equation so we are 0:01:41.400,0:01:47.070 going to multiply P over T right there 0:01:43.409,0:01:52.320 so our first expression PT multiply that 0:01:47.070,0:01:55.860 by P over T P over T and also the K 0:01:52.320,0:01:57.509 multiplied that by K on that side so go 0:01:55.860,0:02:00.299 ahead and multiply the third equation as 0:01:57.509,0:02:03.540 well a fact equation is V over T so 0:02:00.299,0:02:07.259 McCrery by V over T is going to be equal 0:02:03.540,0:02:10.650 to K you multiply that by K also so when 0:02:07.259,0:02:14.709 you multiply those we end up with our 0:02:10.650,0:02:17.200 this and that P times P is P squared 0:02:14.709,0:02:20.049 multiply that by V squared divide that 0:02:17.200,0:02:22.840 by T squared is going to be equal to K 0:02:20.049,0:02:27.370 to the power 3 this is the same as 0:02:22.840,0:02:31.239 saying PV over T all this is squared is 0:02:27.370,0:02:34.319 going to give us K to the power 3 so to 0:02:31.239,0:02:38.469 remove this square sign it becomes PV 0:02:34.319,0:02:43.510 over T this thing is squared is going to 0:02:38.469,0:02:47.139 be equal to K to the power 3 this this 0:02:43.510,0:02:51.310 goes with that you remain with PV over T 0:02:47.139,0:02:54.400 going to give us the square root of K to 0:02:51.310,0:02:58.989 the power 3 now this the square root of 0:02:54.400,0:03:01.180 K to the power 3 is still a constant so 0:02:58.989,0:03:04.599 the ideal gas equation deserves down to 0:03:01.180,0:03:07.449 PV of a t is going to give us a constant 0:03:04.599,0:03:10.030 that is the ideal gas equation now here 0:03:07.449,0:03:13.689 now when we're dealing with one mole of 0:03:10.030,0:03:15.939 0 #Physicsmaths #Physicsmaths