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I just read that carbonic acid turns blue litmus pink and not red.

Is it just because it is a weak acid. What about organic acids then? How do they respond to the litmus test?

If strength and color are related, can we determine the strength of an acid by determining if the litmus paper is more pink or more red?

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Litmus paper will indeed be less or more strongly coloured depending on the pH of the solution you are measuring. Unfortunately though, there is no easy way to quantify it so you cannot use it to semi-accurately determine pH.

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