Molarity (M): The number of moles of solute dissolved in 1 liter of solution. \[ M = \frac{\text{moles of solute}}{\text{volume of solution (L)}}. \] Example: A 1 M solution of NaCl contains 1 mole of NaCl in 1 liter of solution. -
Molality (m): The number of moles of solute dissolved in 1 kg of solvent. \[ m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}}. \] Example: A 1 m solution of NaCl contains 1 mole of NaCl in 1 kg of solvent.
How many molecules are present in 4.4 grams of CO\(_2\)?
(Molar mass of CO\(_2\) = 44 g/mol, Avogadro's number = \(6.022 \times 10^{23}\))
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $