Question

suppose you have a new mountain bike and accidentally spilled a can of carbonated cola on the metallic handlebars and paint. soft drinks (ph = ~2.7) are more acidic than acid rain (ph = ~5.5). about how many times more acidic?
a ~100 times
b ~10,000 times
c ~3 times
d ~1000 times

Explanation:

Step1: Recall the pH formula

The formula for pH is \(pH = -\log_{10}[H^{+}]\), so \([H^{+}]=10^{-pH}\).

Step2: Calculate \([H^{+}]\) for soft - drink and acid rain

For soft - drink with \(pH = 2.7\), \([H^{+}]_{soft - drink}=10^{- 2.7}\).
For acid rain with \(pH = 5.5\), \([H^{+}]_{acid - rain}=10^{-5.5}\).

Step3: Find the ratio of \([H^{+}]\)

The ratio \(\frac{[H^{+}]_{soft - drink}}{[H^{+}]_{acid - rain}}=\frac{10^{-2.7}}{10^{-5.5}}\).
Using the rule of exponents \(a^{m}/a^{n}=a^{m - n}\), we have \(\frac{10^{-2.7}}{10^{-5.5}}=10^{-2.7+5.5}=10^{2.8}\).
Since \(10^{2.8}\approx10^{3}=1000\) (because \(10^{2.8}=10^{3 - 0.2}=\frac{10^{3}}{10^{0.2}}\approx\frac{1000}{1.6}\approx630\), and \(10^{2.8}\) is closer to \(10^{3}\) than other powers of 10 in the options).

Answer:

D. ~1000 times