Step-by-step explanation:
To balance the chemical equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation. Here's how to balance the equation using the algebraic method:
Write the unbalanced equation:
KOH + KNO3 + Cr2O3 -> H2O + K2CrO4 + KNO2
Identify the elements that are not balanced: K, O, Cr, N
Assign a variable to each element that is not balanced. For example, we can assign x to the coefficient for KOH, y to the coefficient for KNO3, and z to the coefficient for Cr2O3:
KOH + KNO3 + Cr2O3 -> H2O + K2CrO4 + KNO2
x y z
Write an equation for each element, using the variables and the coefficients in the unbalanced equation.
For example, for K we have:
x + y + 2z = 2
For O, we have:
x + 3y + 2z = 2
For Cr, we have:
z = 1
For N, we have:
y + z = 1
Solve the system of equations to find the values of x, y, and z. We can use any method to solve the system of equations, such as substitution or elimination. Here's one way to solve the system using substitution:
From the equation for N, we can solve for y: y = 1 - z
Substituting this expression for y in the equation for O, we get:
x + 3(1 - z) + 2z = 2
Simplifying the equation gives us:
x + z = 1
From the equation for Cr, we know that z = 1. Substituting this value in the equation for K, we get:
x + 1 + 2(1) = 2
Solving for x gives us:
x = 0
Substituting the values for x, y, and z back into the unbalanced equation gives us the balanced equation:
0KOH + 1KNO3 + 1Cr2O3 -> 2H2O + 2K2CrO4 + 1KNO2