Logarithm problem, differences

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SUMMARY

The discussion centers on the logarithmic relationship between hydronium ion concentration and pH, specifically the equation pH = -log[H+]. Participants clarify that when two concentrations differ by a factor of 2, the pH difference is represented as -log(√2). The key takeaway is that the difference in pH can also be expressed as log(2), derived from the logarithmic properties of multiplication. The conversation highlights the importance of understanding logarithmic identities in chemistry, particularly in relation to pH calculations.

PREREQUISITES
  • Understanding of logarithmic functions and properties
  • Familiarity with pH and hydronium ion concentration
  • Basic knowledge of algebraic manipulation of logarithms
  • Experience with scientific notation in chemistry
NEXT STEPS
  • Study the properties of logarithms, including product and quotient rules
  • Learn about the relationship between pH and pOH in aqueous solutions
  • Explore logarithmic scales in scientific measurements
  • Review common errors in chemistry solutions manuals and how to identify them
USEFUL FOR

Chemistry students, educators, and anyone involved in scientific calculations that require a solid understanding of logarithmic relationships and pH measurements.

matxjos
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I feel so dumb. I cannot figure out this relationship for the life of me.pH= -log[H+]

Imagine 2 concentrations. If the hydronium ([H+]) concentration differs by a factor of 2, it means the pH of the 2 solutions differs by -log √2

HOW?!
So basically, what they're saying is
(logx)(log√2)=log2x

HOW?
 
Last edited:
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where did you get the sqrt(2) from?

they actually differ by the log(2).

2 * 0.05 = 0.1 and in log form: log(2) + log(0.05) = log(0.1)

hence log(2) = log(0.1) - log(0.05)
 
jedishrfu said:
where did you get the sqrt(2) from?

they actually differ by the log(2).

2 * 0.05 = 0.1 and in log form: log(2) + log(0.05) = log(0.1)

hence log(2) = log(0.1) - log(0.05)


Okay...after more thought, I am convinced my solutions manual is wrong. I hate how many errors are in these things. Thanks jedishrfu.
 

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