Since both solutions are strong acids, we assume complete dissociation. The hydrogen ion concentration in each solution is given by:
[H+]=10−pH. For Solution A
pH=6.0): [H+]A=10−6M For Solution B
(pH=4.0): [H+]B=10−4M. When equal volumes of the two solutions are mixed, the total hydrogen ion concentration in the new solution is the average of the two:
[H+]‌mix ‌=‌=‌. Calculate the numerator:
10−6+10−4=0.000001+0.0001≈0.000101. Then divide by 2 :
[H+]mix≈‌≈5.05×10−5M. [H+]‌mix ‌≈‌≈5.05×10−5M. Now, we convert this concentration back to pH :
pHmix=−log10(5.05×10−5). Breaking the logarithm into parts:
pH‌mix ‌=−[log10(5.05)+log10(10−5)]=−log10(5.05)+5.
Since
log10(5.05)≈0.7, we get:
pH‌mix ‌≈5−0.7=4.3.Thus, the pH of the new solution is approximately 4.3 , which lies between 4 and 5 .
Therefore, the correct answer is:
Option C: between 4 and 5.