Based on the balance equation: 2x + 4y -> 3Z + 5Q and following data, calculate: a) the rate of disappearing of Y b) the rate of disappearing of X c) the rate of appearing of Z d) the rate of appearing of Q e) the overall rate of reaction

The rate of disappearance of Y is given by the negative change in concentration of Y over the change in time.

$$-\frac{\Delta[Y]}{\Delta t} = -\frac{([Y]_{final} - [Y]_{initial})}{(t_{final} - t_{initial})}$$ $$-\frac{\Delta[Y]}{\Delta t} = -\frac{(0.407 \text{ M} - 1.350 \text{ M})}{(11.9 \text{ s} - 0.00 \text{ s})}$$ $$-\frac{\Delta[Y]}{\Delta t} = -\frac{(-0.943 \text{ M})}{11.9 \text{ s}}$$ $$-\frac{\Delta[Y]}{\Delta t} = 0.079243697 \text{ M/s}$$

Rounding to three significant figures:

a) The rate of disappearance of Y: $\boxed{\text{0.0792 M/s}}$

The general relationship between rates for the reaction $2X + 4Y \rightarrow 3Z + 5Q$ is:

$$\text{Rate} = -\frac{1}{2}\frac{\Delta[X]}{\Delta t} = -\frac{1}{4}\frac{\Delta[Y]}{\Delta t} = \frac{1}{3}\frac{\Delta[Z]}{\Delta t} = \frac{1}{5}\frac{\Delta[Q]}{\Delta t}$$

b) The rate of disappearance of X:

$$-\frac{\Delta[X]}{\Delta t} = \frac{2}{4} \times \left(-\frac{\Delta[Y]}{\Delta t}\right)$$ $$-\frac{\Delta[X]}{\Delta t} = \frac{1}{2} \times 0.079243697 \text{ M/s}$$ $$-\frac{\Delta[X]}{\Delta t} = 0.0396218485 \text{ M/s}$$

Rounding to three significant figures: $\boxed{\text{0.0396 M/s}}$

c) The rate of appearing of Z:

$$\frac{\Delta[Z]}{\Delta t} = \frac{3}{4} \times \left(-\frac{\Delta[Y]}{\Delta t}\right)$$ $$\frac{\Delta[Z]}{\Delta t} = \frac{3}{4} \times 0.079243697 \text{ M/s}$$ $$\frac{\Delta[Z]}{\Delta t} = 0.05943277275 \text{ M/s}$$

Rounding to three significant figures: $\boxed{\text{0.0594 M/s}}$

d) The rate of appearing of Q:

$$\frac{\Delta[Q]}{\Delta t} = \frac{5}{4} \times \left(-\frac{\Delta[Y]}{\Delta t}\right)$$ $$\frac{\Delta[Q]}{\Delta t} = \frac{5}{4} \times 0.079243697 \text{ M/s}$$ $$\frac{\Delta[Q]}{\Delta t} = 0.09905462125 \text{ M/s}$$

Rounding to three significant figures: $\boxed{\text{0.0991 M/s}}$

e) The overall rate of reaction:
The overall rate of reaction can be calculated using any species, divided by its stoichiometric coefficient. Using Y:

$$\text{Overall Rate} = -\frac{1}{4}\frac{\Delta[Y]}{\Delta t}$$ $$\text{Overall Rate} = \frac{1}{4} \times 0.079243697 \text{ M/s}$$ $$\text{Overall Rate} = 0.01981092425 \text{ M/s}$$

Rounding to three significant figures: $\boxed{\text{0.0198 M/s}}$