3. Two identical balloons are filled, one with helium and one with nitrogen at the same temperature. If the nitrogen balloon leaks at the rate of 75 mL per hour, what will be the rate of leakage from the helium balloon

140.32mL per hour

Step-by-step explanation:

Rate of leakage of nitrogen ballon = 75 mL/h

Rate of leakage of helium ballon = x

Molar mass of nitrogen= Mn = 14

Molar mass of helium = Mh = 4

Effusion formula

Rate of effusion of helium/ Rate of effusion of nitrogen= √(Molar mass of nitrogen/Molar mass of helium)

Rate of effusion of helium = 75mL/h * √(14/4)

= 140.32mL/h

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!