Hydrochloric acid (chemical formula: HCl) releases hydrogen ions (`H^+` ) when it is dissolved in water. Here we are given some concentration and volume of the acid. We can determine the number of moles of acid from the given information by multiplying the two. That is:

Moles of acid = concentration x volume

= `(0.1 mol)/(dm^3) xx 25 cm^3`

since 1 dm^3 = 1 liter = 1000 cm^3

moles of acid = `(0.1 mol)/(1000 cm^3) xx 25 cm^3`

= 0.0025 moles of acid

Each mole contains an Avogadro's number of ions or atoms or molecules, etc. Avogadro's number is equal to 6.023 x 10^23.

Thus the number of hydrogen ions in the given amount of acid

= 0.0025 moles x 6.023 x 10^23 = 1.51 x 10^21 hydrogen ions

Thus, the given amount of hydrochloric acid contains 1.51 x 10^21 hydrogen ions.

Hope this helps.