To determine which two solutions have similar solubilities at [tex]\(40^{\circ}C\)[/tex], we can look at the known solubility data for each of these substances at that temperature. Let’s investigate each of the given pairs in detail:
1. [tex]\(Na_2SO_4\)[/tex] and NaCl:
- [tex]\(Na_2SO_4\)[/tex] (Sodium sulfate) has a solubility of approximately 21.45 g/100g H[tex]\(_2\)[/tex]O at 40°C.
- NaCl (Sodium chloride) has a solubility of about 36 g/100g H[tex]\(_2\)[/tex]O at 40°C.
- While both are soluble, their solubility values differ noticeably.
2. [tex]\(Na_2HASO_4\)[/tex] and NaCl:
- [tex]\(Na_2HASO_4\)[/tex] (Sodium arsenate) generally exhibits very different solubility characteristics compared to NaCl.
- The solubility value of NaCl remains at approximately 36 g/100g H[tex]\(_2\)[/tex]O, which is distinctive from the expected solubility of [tex]\(Na_2HASO_4\)[/tex].
3. [tex]\(Na_2HASO_4\)[/tex] and [tex]\(Na_2SO_4\)[/tex]:
- Sodium arsenate and sodium sulfate have different chemical structures, leading them to exhibit different solubility behaviors as well.
4. [tex]\(Ba(NO_3)_2\)[/tex] and [tex]\(Ce_2(SO_4)_3 \cdot 9H_2O\)[/tex]:
- [tex]\(Ba(NO_3)_2\)[/tex] (Barium nitrate) and [tex]\(Ce_2(SO_4)_3 \cdot 9H_2O\)[/tex] (Cerium(III) sulfate nonahydrate) each have their own unique solubility profiles.
- Comparing [tex]\(Ba(NO_3)_2\)[/tex] and [tex]\(Ce_2(SO_4)_3 \cdot 9H_2O\)[/tex], they are also likely to have different solubilities due to differing ionic properties and lattice structures.
Given the analysis, the pair of solutions that has similar solubility values at 40°C is:
- [tex]\(Na_2SO_4\)[/tex] (Sodium sulfate) and NaCl (Sodium chloride)
Thus, the answer is the first pair:
[tex]\(Na_2SO_4\)[/tex] and NaCl.
