Question

At 30°C, a substance being dissolved in CCl$_4$ (solvent) exhibits its dissociation half-life as 2.5 hrs. If 256 g of the substance is taken initially, then tell how much of it will remain as such after 20 hrs.

• A. 16 g
• B. 4 g
• C. 1 g
• D. 2 g

Hint:

For half-life problems, use the exponential decay formula to calculate the remaining quantity after a given time.

Answer 1

The Correct Option is C

The half-life of the substance is 2.5 hours. The substance undergoes a dissociation process, which can be modeled by the formula for exponential decay: \[ N = N_0 \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}} \] Where: \( N_0 = 256 \) g (initial amount) \( t_{1/2} = 2.5 \) hrs (half-life) \( t = 20 \) hrs (time elapsed)
Plugging the values into the equation: \[ N = 256 \left(\frac{1}{2}\right)^{\frac{20}{2.5}} = 256 \left(\frac{1}{2}\right)^8 = 256 \times \frac{1}{256} = 1 \text{ g} \] Thus, 1 g will remain, and the rest will have dissociated.