In order to use the Ideal Gas Constant of 0.0821, what units must be used for volume, pressure, amount, and temperature?

The value becomes 0.0821 L-atm/K⁻¹-mol⁻¹.

Explanation:

The value of gas constant is 0.0821.

We know that, the ideal gas law is as follows :

Where

P is pressure

V is volume

T is temperature

In order to use the Ideal Gas Constant of 0.0821, the units are follows :

Volume = Litre (L)

Pressure = atm

Amount = mol⁻¹

Temperature = K⁻¹

So, the value becomes 0.0821 L-atm/K⁻¹-mol⁻¹.

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years

acid rain does not usually kill trees directly. instead, it is more likely to weaken the trees by damaging their leaves, limiting the nutrients available to them, or poisoning them with toxic substances slowly released from the soil. the main atmospheric pollutants that affect trees are nitrates and sulphates.