Question

based on the definition of logarithms, what is the difference in hydrogen ion concentration between a substance with a ph of 2 and a substance with a ph of 3?
a substance with a ph of 3 has a 100 times higher concentration of h+ ions than a substance with a ph of 2.
a substance with a ph of 3 has a 10 times higher concentration of h+ than a substance with a ph of 2.
a substance with a ph of 2 has a 100 times higher concentration of h+ ions than a substance with a ph of 3.
a substance with a ph of 2 has a 10 times higher concentration of h+ than a substance with a ph of 3.

Explanation:

Step1: Formula de pH

El pH se define como \( pH = -\log[H^{+}] \), donde \([H^{+}]\) es la concentración de iones \(H^{+}\). Entonces, \([H^{+}]=10^{-pH}\).

Step2: Concentración para \(pH = 2\)

Para \(pH = 2\), \([H^{+}]_1 = 10^{-2}\).

Step3: Concentración para \(pH = 3\)

Para \(pH = 3\), \([H^{+}]_2 = 10^{-3}\).

Step4: Relación entre concentraciones

Calculemos la relación \(\frac{[H^{+}]_1}{[H^{+}]_2}=\frac{10^{-2}}{10^{-3}} = 10^{-2-(-3)}=10^{1} = 10\). Esto significa que la concentración de iones \(H^{+}\) para \(pH = 2\) es 10 veces mayor que para \(pH = 3\).

Answer:

D. A substance with a pH of 2 has a 10 times higher concentration of \(H^{+}\) than a substance with a pH of 3.