We know the relationship between molality and molarity:
\[\text{Molality} = \frac{1000 \times M}{1000 \times d - M \times (\text{Molar mass of solute})}\]
Substituting the values:
\[3 = \frac{1000 \times x}{1000 \times 1.12 - x \times 40}\]
Rearranging:
\[3 \times (1000 \times 1.12 - x \times 40) = 1000 \times x\]
Simplify:
\[3 \times 1120 - 120x = 1000x\]
\[3360 = 1120x\]
Solving:
\[x = 3\]
Thus, the molarity of the solution is 3.0 M.
Observe the following data given in the table. (\(K_H\) = Henry's law constant)
Gas | CO₂ | Ar | HCHO | CH₄ |
---|---|---|---|---|
\(K_H\) (k bar at 298 K) | 1.67 | 40.3 | \(1.83 \times 10^{-5}\) | 0.413 |
The correct order of their solubility in water is
Match List I with List II:
Choose the correct answer from the options given below:
Let \( S = \left\{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \right\} \), where
\[ A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \]Then \( n(S) \) is equal to ______.