Calculate the mole fraction of solute in the solution if the solution is prepared by dissolving $394 \ g$ of a nonvolatile solute in $622 \ g$ of water at $30^{\circ}C$ (Molar mass of solute $= 342 \ g \ mol^{-1}$).

An aqueous solution of glucose is $10 \%$ in strength. The volume in which $1 \, g-mole$ of it is dissolved will be ............. $L$.

$A$ $40 \%$ by mass sucrose solution is heated till it becomes $50 \%$ by mass. Calculate the mass of water lost from $100 \ g$ of the solution. (in $g$)

What is the mole fraction of the solute in a $1 \, m$ (molal) aqueous solution?

$A$ solution of two components containing $n_{1}$ moles of the $1^{st}$ component and $n_{2}$ moles of the $2^{nd}$ component is prepared. $M_{1}$ and $M_{2}$ are the molecular weights of component $1$ and $2$ respectively. If $d$ is the density of the solution in $g \ mL^{-1}$, $C_{2}$ is the molarity and $x_{2}$ is the mole fraction of the $2^{nd}$ component, then $C_{2}$ can be expressed as

$x$ grams of water is mixed in $69 \ g$ of ethanol. The mole fraction of ethanol in the resultant solution is $0.6$. What is the value of $x$ in grams?