If I threw a block of sodium into a lake, and the H2 created took up 34 L of space at STP (standard temperature and pressure: 1 atm and 0C), how many grams of Na did I begin with?

70g Na

Explanation:

The sodium reacts with water as follows:

2Na + 2H2O → 2NaOH + H2

Where 2 moles of Na produce 1 mole of H2.

To solve this question we must find the moles of H2. With the balanced equation we can find the moles of Na and its mass as follows:

Moles H2:

PV = nRT; n = PV/RT

Where P is pressure = 1atm,

V is volume = 34L,

R is gas constant = 0.082atmL/molK

T is absolute temperature = 273.15K = 0°C

Replacing:

n = 1atm*34L/0.082atmL/molK*273.15K

n = 1.52 moles H2

Moles Na:

1.52 moles H2 * (2mol Na / 1mol H2) = 3.04 moles Na

Mass Na-Molar mass: 22.99g/mol-

3.04 moles Na * (22.99g / mol) =

h let me think

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