Wine goes bad soon after opening because the ethanol in it reacts with oxygen gas from the air to form water and acetic acid , the main ingredient of vinegar. what mass of acetic acid is produced by the reaction of of oxygen gas? round your answer to significant digits.

7.00 g

Explanation:

There is some information missing. I think this is the complete question:

Wine goes bad soon after opening because the ethanol CH₃CH₂OH in it reacts with oxygen gas O₂ from the air to form water H₂O and acetic acid CH₃COOH, the main ingredient of vinegar. What mass of ethanol is consumed by the reaction of 4.86g of oxygen gas? Round your answer to 3 significant digits.

First, we have to write the balanced equation.

CH₃CH₂OH + O₂ ⇒  CH₃COOH + H₂O

Then, we can establish the following relations:

The mass of ethanol that reacts with 4.86 g of oxygen is:

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

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