Ex: Logarithm Application - pH — Transcript
Full transcript
- 0:00- ONE APPLICATION OF A LOG FUNCTION IS THE PH SCALE.
- 0:04THE PH SCALE MEASURES THE ACIDITY OF A SUBSTANCE
- 0:07AND IS DEFINED BY PH EQUALS
- 0:10NEGATIVE THE COMMON LOG OF THE CONCENTRATION OF HYDROGEN IONS
- 0:14MEASURED IN MOLES PER LITER.
- 0:16SO IF A SAMPLE OF MILK HAS A HYDROGEN CONCENTRATION
- 0:18OF APPROXIMATELY 0.0000125 MOLES PER LITER
- 0:25WE CAN FIND THE PH BY SUBSTITUTING THIS VALUE
- 0:28IN FOR THE HYDROGEN ION CONCENTRATION.
- 0:31SO THE PH OF THIS MILK WOULD BE EQUAL TO
- 0:36THE OPPOSITE OR NEGATIVE COMMON LOG OF 0.0000125.
- 0:44AND NOW WE'LL USE THE CALCULATOR TO APPROXIMATE THE PH.
- 0:48SO WE'LL JUST TYPE IN NEGATIVE COMMON LOG
- 0:51AND THEN THE HYDROGEN ION CONCENTRATION.
- 1:00SO THE PH WOULD BE APPROXIMATELY 4.9.
- 1:08NEXT QUESTION IS THE PH OF VINEGAR IS 3.
- 1:11WHAT IS THE HYDROGEN ION CONCENTRATION?
- 1:14SO NOW THEY'RE GIVING US THE PH.
- 1:16WE WANT TO SOLVE THE EQUATION FOR THE CONCENTRATION
- 1:19OF HYDROGEN IONS.
- 1:20SO WE WANT TO SOLVE THE EQUATION
- 1:223 EQUALS NEGATIVE COMMON LOG OF THE HYDROGEN ION CONCENTRATION.
- 1:32NOW WE WANT TO ISOLATE THE LOGARITHM
- 1:33SO WE'LL DIVIDE BOTH SIDES BY -1.
- 1:39THIS IS JUST GOING TO CHANGE THE SIGN
- 1:40ON BOTH SIDES OF THE EQUATION
- 1:42SO NOW WE'LL HAVE -3 EQUALS
- 1:44THE COMMON LOG OF THE HYDROGEN ION CONCENTRATION
- 1:48AND FROM HERE WE NEED TO REMEMBER THAT THE COMMON LOG
- 1:52IS LOG BASE 10.
- 1:53SO NOW TO SOLVE THIS LOG EQUATION
- 1:56WE'LL WRITE THIS AS AN EXPONENTIAL EQUATION.
- 1:58REMEMBER 10 WOULD BE THE BASE, -3 WOULD BE THE EXPONENT
- 2:03AND THE NUMBER WOULD BE THE HYDROGEN ION CONCENTRATION.
- 2:07SO 10 TO THE -3 IS EQUAL TO THE HYDROGEN ION CONCENTRATION.
- 2:14WELL, 10 TO THE -3 CAN BE WRITTEN AS
- 2:181 OVER 10 TO THE POSITIVE 3 POWER
- 2:21WHICH IS EQUAL TO 1 OVER 1,000
- 2:25OR IN DECIMAL FORM 1/1000TH WOULD BE 0.001.
- 2:35THEREFORE THE HYDROGEN ION CONCENTRATION FOR THIS VINEGAR
- 2:39WOULD BE 0.001 MOLES PER LITER
- 2:45WHICH WE COULD EXPRESS WITH A CAPITAL M.
- 2:53OKAY, THAT'S GOING TO DO IT FOR THIS EXAMPLE.
- 2:54I HOPE YOU FOUND THAT HELPFUL.
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