Condition I is false. The reactant concentration does change over time (can be seen the integrated rate law, which has a  term), it just does not depend on the reactant concentration.

Condition II is true. The rate is independent of reactant concentration for 0th order reactions.

Condition III is false.  does have an affect on the overall reactant concentration over time (can be seen by in the integrated rate law, which has a  term).

The only statements that are true are that a plot of ln[A] vs t will be linear for a first order reaction (this can be seen from the integrated rate law given, since the form of the equation is  

With  and  and 

Additionally, for a first order reaction, the rate is proportional to the concentration of [A]. 

All other statements are not true. A plot of [A] vs. t will be exponential.

Michaelis constant, or , is defined as the concentration of substrate at which the reaction rate is half the maximum (). It is a useful measure of how much substrate is needed for reaction to proceed rapidly. A reaction with a high Michaelis constant will need lots of substrate to reach high reaction rates whereas a reaction with low Michaelis constant will need small amounts of substrate to reach high reaction rates. 

Reaction rate, according to Michaelis-Menten model is as follows.

where  is reaction rate,  is maximum reaction rate,  is substrate concentration, and  is the Michaelis constant. If we analyze the given options, we will observe that the greatest increase in  occurs when  is doubled (increased by a factor of 2). Increasing substrate concentration by a factor of 2 will have nearly the same effect; however, since  is also found in the denominator it will only slightly contribute to an increase in .

Note that the units for  is molarity,  is molarity, and  is . Solving for  will give us units of .

To solve this problem we need to use the Michaelis-Menten equation.

where  is reaction rate,  is maximum reaction rate,  is substrate concentration, and  is the Michaelis constant. If we plug in the given values we get a reaction rate of

Note that the Michaelis-Menten equation implies that the  will never exceed . Regardless of how high the substrate concentration is, the reaction rate will approach  but will never equal or exceed it. You can try this by substituting very high values for substrate concentration. The  will get very close to 0.2 () but will never equal or exceed it.

The Michaelis-Menten equation is as follows.

Where  is reaction rate,  is maximum reaction rate,  is substrate concentration, and  is the Michaelis constant. Since the Michaelis constant, , is in the denominator, the reaction rate is inversely proportional to the Michaelis constant; therefore, increasing the Michaelis constant will decrease the reaction rate.

Catalysts are added to a reaction to decrease the activation energy. This will allow for reactants to easily overcome the energy barrier (activation energy) and carry out the reaction; therefore, the reaction will happen quicker and the rate of reaction will increase. Recall that the rate constant quantifies the rate of a reaction. Since rate of reaction and rate constant are directly proportional, addition of catalyst will lower the activation energy, increase the rate of reaction, and, subsequently, increase the rate constant.

It’s important to remember that catalysts only alter the rate of a reaction (speeds up the reaction). They have no effect on thermodynamics/equilibrium (the amount of products produced).

The speed of a reaction is increased when the amount of reactants reaching the activation energy (energy barrier) is increased. This can be done via two ways: increasing temperature or adding a catalyst. Increasing temperature will add kinetic energy to the reactant and increase the amount of reactants reaching the energy barrier. Adding a catalyst will decrease the activation energy and, subsequently, increase the amount of reactants reaching the energy barrier.

Since the temperature is kept relatively constant in the human body (due to homeostasis), the most common way human body increases the speed of a reaction is by using catalysts. Biological catalysts are called enzymes and they are usually named with the suffix -ase. The only molecule that is an enzyme in this question is DNAase, which catalyzes the hydrolysis of phosphodiester bonds in the backbone of DNA.

ATP provides energy for active reactions but it cannot speed up the reaction. Histones are proteins found in nucleus that are involved in DNA packaging. They are irrelevant to this question.

Catalysts are chemicals that function to speed up a reaction. They do not, however, change the amount of products produced (the equilibrium of the reaction). They just make it so that the equilibrium is reached at a faster rate. The main way catalysts decrease reaction rate is by lowering the activation energy. This is the energy peak required to create transition states (molecules that are in between reactants and products). Once past this peak, the transition states convert into the products. Catalysts lower this peak so that it is easier to create transition states.

As mentioned, equilibrium constant will not change because catalysts do not alter the equilibrium of the reaction. Enthalpy (change in heat) of the reaction will also remain constant because it is not altered by the catalyst.

An adiabatic reaction is characterized as a reaction that neither gains nor loses net heat. This means that the process of converting the reactants to products does not alter the heat in the system (reaction) or the surroundings; therefore, both the heat inside and outside the system will be constant.