Suppose 2.00 mol of an ideal, monatomic gas is initially at a pressure of 3.00 atm and a temperature T = 350 K. It is expanded irreversibly and adiabatically (q = 0) against a constant external pressure of 1.00 atm until the volume has doubled. A. Calculate the final volume.
B. Calculate w, q and ?U for this process , in joules.

a) the final volume is 38.285 L

b)

w = - 1839.158 J,

q = 0,

ΔU = - 1839.158 J

Explanation:

Given that;

number of moles n = 2

initial pressure p1 = 3 atm

external pressure p_ext = 1 atm

temperature T1 = 350 k

we know that gas constant R = 8.315 JK⁻¹mol¹ = 0.08206 L atm K⁻¹ mol⁻¹

a)

to determine the initial volume , we use the equation for ideal gas;

V1 = nRT1/p1

so we substitute

V1 = (2 × 0.08206 × 350) / 3

V1 = 57.442 . 3

V1 = 19.147 L

given that, the gas is expanded irreversibly and adiabatically until the volume has doubled;

so Final volume v2 will be;

V2 = 2 × V1

V2 = 2 × 19.147 L

V2 = 38.285 L  

Therefore, the final volume is 38.285 L

b)

to determine w, q and U;

we know that, work done in gas expansion at a constant speed is expressed in the following equation;

w = -p_ext ΔV

where ΔV is change in volume

so we substitute

w = -( 1 atm) ( 38.285 L - 19.147 L)

w = -( 1 atm) ( 19.138 L)

w = -(19.138 L-atm)

we know that 1 L-atm = 101.325 J.

so

w = -(19.138 × 101.325 J)

w = - 1839.158 J

now, since there is no transfer of heat into or out of the system for the adiabatic process;

q = 0

using the first law of thermodynamics, changes in internal energy will be;

ΔU = q + w

we substitute

ΔU = 0 + ( - 1839.158 J )

ΔU = - 1839.158 J

alkaline metals are lithium, sodium, rubidium, potassium, cesium and francium.

alkali metals have electronegativity from 0.7 to 1, lowest in periodic table of elements, which means that alkali metals (i group in periodic table) has positive oxidation number in compounds.

electronegativity is a chemical property that describes the tendency of an atom to attract a shared pair of electrons towards itself.

alkaline metals (far left in main group) have lowest ionizations energy and easy remove valence electrons,

for example, potassium is the alkali metal and has a single valence electron in the outer electron shell.

electron configuration of potassium is: ₁₉k 1s²2s²2p⁶3s²3p⁶4s¹.

they can not exist alone in nature, because they are very reactive.