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Test Prep MCAT Test Exam
Medical College Admission Test: Verbal Reasoning, Biological Sciences, Physical Sciences, Writing Sample (Page 12 )

Updated On: 25-Jan-2026
Page 12 of 164
PDF with 811 Questions

One of the most common methods that scientists use to determine the age of fossils is known as carbon dating. 14C is an unstable isotope of carbon that undergoes beta decay with a half-life of approximately 5,730 years. Beta decay occurs when a neutron in the nucleus decays to form a proton and an electron which is ejected from the nucleus.
14C is generated in the upper atmosphere when 14N, the most common isotope of nitrogen, is bombarded by neutrons. This mechanism yields a global production rate of 7.5 kg per year of 14C, which combines with oxygen in the atmosphere to produce carbon dioxide. Both the production and the decay of 14C occur simultaneously. This process continues for many half-lives of 14C, until the total amount of 14C approaches a constant.
A fixed fraction of the carbon ingested by all living organisms will be 14C. Therefore, as long as an organism is alive, the ratio of 14C to 12C that it contains is constant. After the organism dies, no new 14C is ingested, and the amount of 14C contained in the organism will decrease by beta decay. The amount of 14C that must have been present in the organism when it died can be calculated from the amount of 12C present in a fossil. By comparing the amount of 14C in the fossil to the calculated amount of 14C that was present in the organism when it died, the age of the fossil can be determined.
The bones of a living human adult contain about 8 grams of 14C at any given time. If a prehistoric human adult skeleton is found to contain 1 gram of 14C, what is the approximate age of the fossil?

  1. 5,730 years
  2. 17,190 years
  3. 34,380 years
  4. 45,840 years

Answer(s): A

Explanation:

The passage states that after death, the 14C in a skeleton that beta decays is not replaced by new 14C.
Consequently, as time passes, the amount of 14C in the skeleton decreases.
The half-life quantifies the rate of this decrease. The half-life of an isotope is the length of time it takes for half of the atoms in a sample of that isotope to decay. A skeleton starts out with 8 g of 14C, and the half-life of 14C is 5,730 years. Therefore, after 5,730 years, 8 g of 14C will decay to 4 g. After another 5,730 years, 4 g will decay to 2 g, and after yet another 5,730 years, 2 g will decay to 1 g, which is the amount present in the prehistoric skeleton. Hence, the prehistoric skeleton must be 3(5,730) = 17,190 years old, and choice B is correct.



A researcher investigated the equilibrium between CO2, C, and CO as a function of temperature. The equation is given below:

Carbon dioxide, at 298 K and 1 atm, and an excess of powdered carbon were introduced into a furnace, which was then sealed so that pressure would increase as the temperature rose. The furnace was heated to, and held constant at, a predetermined temperature. The pressure within the furnace chamber was recorded after it had remained unchanged for one hour. The table below shows the pressures recorded for a series of temperatures together with the pressures expected if no reaction had taken place.
Table 1


When the system stabilized at 1,200 K, a sample of helium was injected into the furnace. What should happen to the amount of carbon dioxide in the system?

  1. It should increase.
  2. It should decrease.
  3. It should be completely converted to carbon monoxide.
  4. It should remain the same.

Answer(s): D

Explanation:

You should know that helium, a noble gas, is very unreactive and would almost certainly not react with any of the species in the furnace. Because the helium does not react with any of the species that participate in the equilibrium, the equilibrium is unaffected by the addition of helium. Even though it increases the total pressure inside the system, the partial pressures of the reacting gases are unchanged (Dalton's law) and therefore they keep on behaving as if the helium weren't present. The correct choice is therefore choice D.



A researcher investigated the equilibrium between CO2, C, and CO as a function of temperature. The equation is given below:

Carbon dioxide, at 298 K and 1 atm, and an excess of powdered carbon were introduced into a furnace, which was then sealed so that pressure would increase as the temperature rose. The furnace was heated to, and held constant at, a predetermined temperature. The pressure within the furnace chamber was recorded after it had remained unchanged for one hour. The table below shows the pressures recorded for a series of temperatures together with the pressures expected if no reaction had taken place.
Table 1


What can be said about the value of S° of the reaction?

  1. It is positive.
  2. It is negative.
  3. It is zero.
  4. It cannot be determined from the information given.

Answer(s): A

Explanation:

The entropy of a reaction is a measure of the disorder of the system. The sign of the value of the entropy indicates whether the products of a reaction are more or less disordered than the reactants. A reaction that experiences an increase in disorder in going from reactants to products would have a positive S for the reaction. Similarly, a reaction that decreases its disorder would have a negative S for the reaction. In this reaction, 1 mole of carbon dioxide, a gas, reacts with 1 mole of solid carbon to give two moles of carbon monoxide gas. Since there are more moles of gas in the products than in the reactants, there is an increase in entropy, meaning that the sign of the change is positive. Choice A is therefore the correct response.



A researcher investigated the equilibrium between CO2, C, and CO as a function of temperature. The equation is given below:

Carbon dioxide, at 298 K and 1 atm, and an excess of powdered carbon were introduced into a furnace, which was then sealed so that pressure would increase as the temperature rose. The furnace was heated to, and held constant at, a predetermined temperature. The pressure within the furnace chamber was recorded after it had remained unchanged for one hour. The table below shows the pressures recorded for a series of temperatures together with the pressures expected if no reaction had taken place.
Table 1


How many pi bonds are in the carbon dioxide molecule?

  1. 0
  2. 1
  3. 2
  4. 3

Answer(s): C

Explanation:

The carbon dioxide molecule has a central carbon bonded to two oxygen atoms: carbon shares two electrons with each oxygen, and each oxygen shares two electrons with carbon. As a result of this sharing pattern, two double bonds are formed. You should know that a double bond consists of one sigma bond and one pi bond.
Since there are two double bonds, there are two pi bonds, making choice C the correct choice.



A researcher investigated the equilibrium between CO2, C, and CO as a function of temperature. The equation is given below:

Carbon dioxide, at 298 K and 1 atm, and an excess of powdered carbon were introduced into a furnace, which was then sealed so that pressure would increase as the temperature rose. The furnace was heated to, and held constant at, a predetermined temperature. The pressure within the furnace chamber was recorded after it had remained unchanged for one hour. The table below shows the pressures recorded for a series of temperatures together with the pressures expected if no reaction had taken place.
Table 1


Which of the following is NOT necessarily true about the equilibrium reaction between CO2, C, and CO?

  1. The standard entropy change is positive.
  2. A decrease in pressure at constant temperature would shift the equilibrium to the right.
  3. Addition of CO will shift the equilibrium to the left.
  4. The standard Gibbs' free energy change is negative.

Answer(s): D

Explanation:

You should know the relationship G = H - TS. S for this reaction is positive, because there are more moles of gaseous products than reactants, but there is no information about the sign of H. Since H cannot be determined, neither can G. Choice D is the correct response. Choice A is wrong (that is, the statement is certainly true) because, as was just stated, the entropy change is positive. Choice B is wrong because, according to Le Châtelier's principle, a decrease in pressure will favor the side of the reaction with more moles of gas. In this case, it is the products side, and the equilibrium is said to have shifted to the right. Choice C is wrong because, again, according to Le Châtelier's principle, addition of a product will shift the equilibrium to the left, that is, the reactants side.



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