Can anybody suggest me how can I calculate the activity of water in solution of water, salt and acid without calculating the vapor pressure of the water and partial pressure of aqueous salt and acid solution.
The activity coefficients of the liquids and their partial pressures are directly related through thermodynamic principles. When you have one, you can determine the other.
You can find more information about the relationships as well as how to measure and calculate the values in the chapters on solutions in an undergraduate-level textbook for physical chemistry. I recommend the authors Atkins or Silbey or Levin or ... any other. Indeed, I think your question is similar to some of the homework problems that are given in these same textbooks.
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