Isotonic solutions have the same osmotic pressure. The osmotic pressure ($\pi$) is given by:
\[ \pi = CRT \]
where C is the molar concentration, R is the gas constant, and T is the temperature.
For isotonic solutions, $\pi_1 = \pi_2$, so:
\[ C_1RT = C_2RT \]
Since R and T are the same for both solutions, we have $C_1 = C_2$.
First, let's calculate the molar concentration of the urea solution:
Molar mass of urea (NH$_2$CONH$_2$) = (2 $\times$ 14) + (4 $\times$ 1) + 12 + 16 = 60 g/mol
Concentration of urea ($C_1$) = $\frac{mass}{molar mass \times volume} = \frac{15 g}{60 g/mol \times 1 L} = 0.25$ M
Now, we know the molar concentration of the glucose solution must also be 0.25 M. We can use this to calculate the mass of glucose needed:
Molar mass of glucose (C$_6$H$_{12}$O$_6$) = (6 $\times$ 12) + (12 $\times$ 1) + (6 $\times$ 16) = 180 g/mol
Mass of glucose (m) = $C_2 \times molar mass \times volume = 0.25 M \times 180 g/mol \times 1 L = 45$ g
If \(A_2B \;\text{is} \;30\%\) ionised in an aqueous solution, then the value of van’t Hoff factor \( i \) is:
1.24 g of \(AX_2\) (molar mass 124 g mol\(^{-1}\)) is dissolved in 1 kg of water to form a solution with boiling point of 100.105°C, while 2.54 g of AY_2 (molar mass 250 g mol\(^{-1}\)) in 2 kg of water constitutes a solution with a boiling point of 100.026°C. \(Kb(H)_2\)\(\text(O)\) = 0.52 K kg mol\(^{-1}\). Which of the following is correct?
List I | List II | ||
A | Down’s syndrome | I | 11th chormosome |
B | α-Thalassemia | II | ‘X’ chromosome |
C | β-Thalassemia | III | 21st chromosome |
D | Klinefelter’s syndrome | IV | 16th chromosome |
The velocity (v) - time (t) plot of the motion of a body is shown below :
The acceleration (a) - time(t) graph that best suits this motion is :