In reactions involving oxides and water, carefully balance the equations and count the atoms to ensure accuracy in stoichiometry
The reactions of sodium oxide and dichlorine heptoxide with water are as follows:
\[ Na_2O + H_2O \rightarrow 2NaOH \]
\[ Cl_2O_7 + H_2O \rightarrow 2HClO_4 \]
Adding the coefficients from both equations: 1 +4=5
The colour of the solution observed after about 1 hour of placing iron nails in copper sulphate solution is:
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.