32
40
We are given that the concentration of the nitric acid solution is 75% by mass. This means that for every 100 g of solution, there are 75 g of nitric acid. We are asked to find the volume of the solution that contains 30 g of nitric acid. First, calculate the total mass of the solution required to get 30 g of nitric acid: \[ \text{Mass of solution} = \frac{30 \, {g}}{0.75} = 40 \, {g} \] Now, using the density of the solution, which is 1.25 g/mL, calculate the volume of the solution: \[ \text{Volume} = \frac{40 \, {g}}{1.25 \, {g/mL}} = 32 \, {mL} \] Thus, the volume required is 32 mL.
The freezing point depression constant (\( K_f \)) for water is \( 1.86 \, {°C·kg/mol} \). If 0.5 moles of a non-volatile solute is dissolved in 1 kg of water, calculate the freezing point depression.
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 ______.
Two vessels A and B are connected via stopcock. Vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel A expands into vessel B and no change in temperature is observed in the thermometer. Which of the following statement is true?
Choose the correct nuclear process from the below options:
\( [ p : \text{proton}, n : \text{neutron}, e^- : \text{electron}, e^+ : \text{positron}, \nu : \text{neutrino}, \bar{\nu} : \text{antineutrino} ] \)
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: