1) a certain amount of chlorine gas was placed inside a cylinder with a movable piston at one end. the initial volume was 3.00 l \rm l and the initial pressure of chlorine was 1.45atm the piston was pushed down to change the volume to 1.00 lcalculate the final pressure of the gas if the temperature and number of moles of chlorine remain constant..
2) in an air-conditioned room at 19.0c a spherical balloon had the diameter of 50.0 cm when taken outside on a hot summer day, the balloon expanded to 51.0cm cm in diameter. what was the temperature outside? assume that the balloon is a perfect sphere and that the pressure and number of moles of air molecules remains the same.

1) 4.35 atm

2) 36.88 °C

Explanation:

1) Because the temperature and number of moles remained constant, we can use the formula P₁V₁=P₂V₂

3.00 L * 1.45 atm = P₂ * 1.00 L

P₂ = 4.35 atm

2) First we use a geometrical formula to calculate the volume of the spherical balloon when it has a diameter of 50.0 and of 51.0 cm.

V₁ = 4/3 * π*(50/2)³ = 65449.85cm³

V₂ = 4/3 * π*(51/2)³ = 69455.90cm³

Then we use T₁V₂=T₂V₁, keeping in mind using Kelvin as the unit for temperatures:

292.16 K *  69455.90cm³ = T₂ * 65449.85cm³

T₂ = 310.04 K = 36.88 °C

answer: the figure is attached herewith.

step-by-step explanation:   we are given to sketch a unit circle and label the terminal points corresponding to

in the attached figure, we have drawn a unit circle, with centre at o(0,0) and radius 1 unit. we have labelled the points a, b, c, d and e corresponding to the angles below

∠aox = 60°,

∠box = 120°,

∠cox = 180°,

∠dox = 240°,

∠eox = 300°.

and the coordinates are a(0.5,1), b(-0.5,1), c(-1,0), d(-0.5,-1) and e(0.5,-1).

thus, the answer is complete.

the increase of protons   hope this