Final answer:
To find the solutions with the same number of hydrogen ions as in 50 cm^3 of 0.1 mol dm^-3 sulfuric acid, we calculate the number of moles of hydrogen ions in each solution. Only solution I and III have the same number of hydrogen ions.
Step-by-step explanation:
To determine which of the solutions have the same number of hydrogen ions as in 50 cm3 of 0.1 mol dm-3 sulfuric acid, we need to calculate the number of moles of hydrogen ions for each solution.
I. 100 cm3 of 0.1 mol dm-3 hydrochloric acid: Since the concentration is the same as the sulfuric acid, it would have the same number of moles of hydrogen ions.
II. 50 cm3 of 0.2 mol dm-3 nitric acid: To find the number of moles of hydrogen ions, we multiply the volume (in dm3) by the molarity. Therefore, it would have 0.2 mol dm-3 x 0.05 dm3 = 0.01 mol of hydrogen ions.
III. 100 cm3 of 0.2 mol dm-3 sulfuric acid: Similar to sulfuric acid, it would have the same number of moles of hydrogen ions.
IV. 50 cm3 of 0.1 mol dm-3 phosphoric acid: We multiply the volume (in dm3) by the molarity to find the number of moles of hydrogen ions. Therefore, it would have 0.1 mol dm-3 x 0.05 dm3 = 0.005 mol of hydrogen ions.
Based on the calculations, only solution I and III have the same number of hydrogen ions as in 50 cm3 of 0.1 mol dm-3 sulfuric acid.