Mayor Bloomberg’s “Soda Ban” has become a reality. The ban was proposed to help curb the epidemic of obesity in the city. But is it a ban? Not really. It’s a cap placed on the size of beverages. You can still buy 2 or more beverages if you like.

Previously, the Mayor had championed a general smoking ban in public spaces that included parks and plazas. This was largely based on the idea that it was in the interest of public health and other municipalities have seen positive outcomes. One example of such improvement over public health after a smoking ban comes from Pueblo, Colorado where a 27% decrease in heart attack cases resulted from a ban while surrounding municipalities had unchanged rates.

The large beverage cap was a discussion on a recent Science Friday. Do you think we will see public health benefits from a beverage cap? Check out the discussion on Science Friday and figure out where you fit in on the debate. Do you see this figuring in to ameliorating the obesity issue? Will the public truly benefit from this? What do you think about the marketing campaign and the formation of artificial grassroots movements that are sponsored by the American Beverage Association who benefit from the increased sales of their product?

This year marks the 50th anniversary of the publication of Silent Spring. In this book, Rachel Carson, described the bleak future that could possibly exist based on the changes to the environment that human activity was causing. Specifically, she warned about the dangers of pest control in the chemical called DDT. She urged the public to consider the consequences of using chemicals like this that were taking a toll on predatory birds, often apex predators in their ecosystems. While DDT is a neurological toxin specific to arthropods (intended to control mosquito populations), the chemical accumulated within the environment and would biomagnify in predatory birds where it was deleterious to various systems and resulted in a thinning of egg shells that caused the destruction of eggs. Apex predators often serve as sentinels for the health of the environment. As peregrine falcon populations became extirpated, the reality of a silent Spring was becoming apparent to the public. 10 years after the publication of her book, the United States government banned the use of DDT.

The population of Peregrine Falcons has rebounded and they are no longer on the endangered species list. Many often adapt to city dwelling. Below is a picture of nestling falcons readying to fledge at Riverside Church.

Criticizing Silent Spring

Despite the success of the DDT ban and the improved healthiness of local environments, the book often found criticisms. Below is a review of the book from Amazon.com by a user called “Jane Orient”:

DDT was actually good for birds. There is a vast amount of material to refute assertions to the contrary. Bird counts in 1960 (after DDT) vs. 1941 (before DDT) showed 12 times more robins, 21 times more cowbirds, 38 times more blackbirds, 131 times more grackles, etc. Possible protective effects include: increasing plant yields; increasing protective cover; eliminating mosquito-borne bird diseases; and inducing liver enzymes that break down naturally occurring environmental toxins and carcinogens.

Sometimes we see claims that are true in nature that are actually “truthy“. The claim indicates that DDT usage was good for birds and cites some real facts regarding the increased number of birds. While these facts may be real, anyone with a shred of intelligence would point out that they are all prey species and that the decimation of predator species like the Peregrine Falcon resulted in a population explosion. Misleading people with true statements followed by unverifiable statements can often confuse and sway lay people who are not familiar with the argument. By beginning with true facts, the reviewer has augmented the subsequent baseless claims about toxicity. The greatest argument against Silent Spring follows from the same reviewer:

This is one of the most influential books of our time. Even now, it contributes to the death of one child every 12 seconds, mostly in the Third World, because it helped to bring about the ban of DDT with a resulting resurgence of malaria and other insect-borne diseases.

Rachel Carson herself stated:

It is not my contention that chemical insecticides must never be used. I do contend that we have put poisonous and biologically potent chemicals indiscriminately into the hands of persons largely or wholly ignorant of their potentials for harm. We have subjected enormous numbers of people to contact with these poisons, without their consent and often without their knowledge.

Additionally, the DDT ban in 1972 was for the United States. DDT was still manufactured in the U.S. and utilized elsewhere. DDT simply fell out of favor since it was becoming less effective.

Revisiting Silent Spring

As humans, we often have huge impacts on our local environments. The city is a densely populated space and we have created a waste issue. This waste has resulted in the explosion of invasive rodent species. As a consequence, public and private spaces have taken to using anti-coagulant baits instead of addressing waste and sanitation issues. The consequences can be seen below:

The report that accompanied this photo and related hawk deaths in the month of March 2012 indicate that multiple types of anticoagulant rodenticides resulted in spontaneous hemorrhaging or bleeding caused by stress of egg-laying.

Above is a picture of a female red-tailed hawk nesting in Riverside Park. Below is a picture of her from the necropsy report. She died from hemorrhaging following laying an egg.

Acids and Bases

We can call any compound that adds H⁺ ions (a free proton) into solution an acid. Along with this, we would expect that any compound that would decrease the concentration of free H⁺ of a solution as a base. pH is the power of H⁺ of a solution. We define this power as a molar concentration of H⁺ in solution. This concentration invariably ends up being a relatively small number (though great in absolute numbers) and is expressed as a decimal number. Because the range of the concentrations is so great, we express these numbers as logarithmic numbers to avoid writing many 0’s after the decimal and to facilitate communicating the concentration. Since these numbers are so (relatively) small, we use the negative logarithm to describe this concentration.

Mathematically defined, pH = -Log₁₀[H⁺]

The pH scale ranges so that anything below pH 7 is acidic and anything above pH 7 is alkaline. So a smaller number is more acidic. But didn’t we just state that something acidic contains more H⁺ ions? Remember, because we are dealing with a negative Logarithm, this means the concentration is higher.

Now you’re just talking crazy!

If we have a quantity that is 10², we know that translates into 100. Just as if we have a quantity of 10⁴, we know that translates into 10000. Just as it becomes inconvenient to keep writing all those 0’s, it’s really impractical to write many many 0’s after a decimal. It’s really hard to talk about too! So we likewise will express numbers like 0.0001 as 10^-4. A logarithm is the reverse function of an exponent. More precisely, the logarithm of a number is the exponent by which the base has to be raised to produce that number. Therefore:

• Log₁₀(0.0001) = -4
• Log₁₀10^-4 = -4

So how do we define a solution that is pH 2? Well, we already decided that this solution is below pH 7 — making it an acid. But what does this mean in terms of H⁺ ion concentration?
Let’s work this out algebraically:

• pH = -Log₁₀[H⁺] Let’s bring the (-) over to the other side by multiplying both sides by -1
• -(pH) = Log₁₀[H⁺] Now let’s reverse the Log → base 10 remembering that logarithms are opposite functions of exponents
• 10^-(pH) = [H⁺] Plug in the pH → molar concentration of [H⁺]

As we can now see, a solution of pH 2 is acidic because the molar concentration of [H⁺] is 10^-2mole/L or 0.01M

You’re still talking crazy! That number is small!

It’s not a small number. Remember that a mole is 6.022 X 10²³. That’s a very large number! Think about it! A solution of pH 4 is acidic, but if we plug in the formula, we realize that this is equal to 0.0001M H⁺ – less than pH 2 at 0.01M!

But let’s compare it to the [H⁺] content of H₂O. Now I’m going to sound crazier! Water can be thought of as being in an equilibrium where some of the molecules are ionizing and deionizing. We can express this in 2 ways:

• H₂O ⇋ H⁺ + OH^–
• 2H₂O ⇋ H₃O⁺ + OH^–

So at any given point, a liter of H₂O at neutral pH (7) has 10^-7 moles of H⁺ ions. Incidentally, it also has 10^-7 moles of OH^– in solution. The second expression indicates the formation of a hydronium ion (H₃O⁺) instead of a free proton in solution. So something that is pH 2 is a stronger acid than pH 4, right? Nope. That just indicates the amount of free protons in solution. It is more acidic but acid strength means something else. When we talk about strong acids, it means that it is more likely to donate a proton to the solution because it is more likely to ionize. Let’s look at the following:

• HA ⇋ H⁺(aq) + A^–(aq) Where HA is an acid dissociating in solution

If this dissociation is very high, then we say that it is a strong acid. Similarly, a compound like NaOH readily dissociates completely in solution and provides OH^– ions that can readily remove H⁺ from solution –a strong base! We speak of dissociation in terms of rates and we express this as the acid dissociation constant, K_a. This is calculated using the concentrations of [H⁺] (proton), [A^–] (conjugate base) and [HA] (non-dissociated) at equilibrium:

• K_a = ([H⁺][A^–])/[HA]

Just like the orders of magnitude we have when discussing pH, the rates of dissociation are more conveniently communicated on a logarithmic scale.

• pK_a = -Log₁₀K_a

Think about it this way, if the concentration of the dissociated ions is very high, the numerator in the rate is very high → K_a is great. In other words, at equilibrium, the dissociation reaction looks more unidirectional than bi-directional as the compound is readily ionized:

• HA → H⁺(aq) + A^–(aq)

On this scale, we refer to anything with a pK_a < -2 as a strong acid since it will readily dissociate in solution. This form of the dissociation constant is extremely useful in estimating the pH of buffer solutions and for finding the equilibrium pH of the acid-base reaction (between the proton and the conjugate base). We can estimate the pH by utilizing the Henderson-Hasselbalch Equation:

• pH = pK_a + Log₁₀([A^–]/[HA])

Titration of a Weak acid by a strong Base

So what happened in lab when we titrated our Acetic acid (a weak acid)? Check out this video from the Khan Academy that explains the change in dissociation of the weak acid as the protons are continuously removed from solution by the NaOH