$4 g$ equimolar mixture of $NaOH$ and ${Na}_2{CO}_3$ contains $x g$ of $NaOH$ and $yg$ of ${Na}_2{CO}_3$. The value of $x$ is ____ g. (Nearest integer)

Suppose the weight of $NaOH$ being $w_1 g$ and the weight of ${Na}_2{CO}_3$ being $w_2 g$.

The molar mass of $NaOH$ is $40 g/mol$

The molar mass of ${Na}_2{CO}_3$ is $106 g/mol$

Here, $w_1+w_2=4$

For an equimolar mixture,

$$\begin{gathered} \frac{w_1}{40}=\frac{w_2}{106} \\ \Rightarrow \frac{w_1}{40}=\frac{4-w_1}{106} \\ \Rightarrow 160-40w_1=106w_1 \\ \Rightarrow 160=106w_1+40w_1 \\ \Rightarrow 146w_1=160 \\ \Rightarrow w_1=\frac{160}{146} \\ \Rightarrow w_1=1.096 g \end{gathered}$$

The weight of $NaOH$ is $1.096 g$.

Hence the correct answer is 1.096.