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The plant was placed in a dark cupboard for two days to destarch it. In darkness, photosynthesis cannot occur, so the plant cannot produce new starch. Instead, it continues to respire, using up any stored starch in its leaves. After two days, the leaves should have little to no starch remaining.

When the leaf is later placed in bright sunlight (even inside a clear plastic bag), it can carry out photosynthesis again because it now has light and still has carbon dioxide (trapped inside the bag and also produced by respiration). During these few hours, the leaf will produce glucose, which is then converted into starch and stored in the leaf.

Result of the starch test:

The leaf will test positive for starch (it will turn blue-black with iodine solution).

Reasoning:

Darkness → starch used up (destarching)

Light → photosynthesis resumes → new starch produced

Therefore, starch is present after sunlight exposure.

This experiment is a classic setup to test the requirements for photosynthesis. Here is the breakdown of why these steps were taken and what the results would be.

1. Why the plant was placed in a dark cupboard

The plant was placed in the dark for two days to destarch it.

The Process: In the absence of light, a plant cannot perform photosynthesis to produce new glucose. However, the plant still needs energy for cellular respiration to stay alive.

The Result: It consumes its stored reserves of starch (converting it back into glucose for energy). By the end of the 48 hours, the plant has "emptied" its starch stores, ensuring that any starch found later in the experiment was produced during the experiment and wasn't already there.

2. The Result of the Starch Test

If the student tests this specific leaf for starch using iodine solution, the result will be negative (the iodine will remain yellow-brown and will not turn blue-black).

3. Reasoning

Even though the leaf was placed in bright sunlight—which usually allows for photosynthesis—it was sealed inside a clear plastic bag.

Carbon Dioxide Limitation: Photosynthesis requires two primary raw materials: water and carbon dioxide.

The Sealed Environment: By sealing the leaf in a bag after it had been destarched, the amount of CO₂ available is limited to the tiny amount trapped inside the bag. This small amount is quickly exhausted.

No New Starch: Without a continuous supply of CO₂ from the atmosphere, the leaf cannot synthesize glucose, and therefore cannot convert excess glucose into starch.

Conclusion: Since the leaf started with no starch (due to the dark cupboard) and could not produce new starch (due to the lack of CO₂ in the bag), the starch test will show that no starch is present.

Let Ahmad initially have A cards and Bala have B cards.

We know: A + B = 144

Step 1: Ahmad gives 1/4 of his cards to Bala

Ahmad gives (1/4)A, so:

Ahmad now has (3/4)A

Bala now has B + (1/4)A

Step 2: Bala gives 1/3 of his new total to Ahmad

Bala gives (1/3)(B + (1/4)A)

After this:

Bala has: (2/3)(B + (1/4)A)

Ahmad has: (3/4)A + (1/3)(B + (1/4)A)

Step 3: They end up with equal amounts

(3/4)A + (1/3)(B + (1/4)A) = (2/3)(B + (1/4)A)

Simplifying:

Left side: (3/4)A + (1/3)B + (1/12)A = (10/12)A + (1/3)B = (5/6)A + (1/3)B

Right side: (2/3)B + (1/6)A

Set equal: (5/6)A + (1/3)B = (1/6)A + (2/3)B

Rearrange: (4/6)A = (1/3)B → (2/3)A = (1/3)B → B = 2A

Step 4: Use total

A + B = 144 → A + 2A = 144 → 3A = 144 → A = 48

Answer: Ahmad had 48 game cards at first.

To find out how many cards Ahmad had at first, we can work backward from the final state.

Step 1: Determine the final state

The total number of cards is 144. Since they ended up with the same number of cards:

Ahmad's final cards: 144 ÷ 2 = 72

Bala's final cards: 144 ÷ 2 = 72

Step 2: Reverse Bala's gift to Ahmad

Before the final state, Bala gave 1/3 of his total cards to Ahmad.

If Bala gave away 1/3, he was left with 2/3 of his total.

2/3 of Bala's total = 72

1/3 of Bala's total = 72 ÷ 2 = 36

Bala's total (before giving to Ahmad) = 36 × 3 = 108

Since Bala gave 36 cards to Ahmad, we must subtract those from Ahmad's final total:

Ahmad's cards (before receiving from Bala) = 72 - 36 = 36

Step 3: Reverse Ahmad's gift to Bala

Initially, Ahmad gave 1/4 of his cards to Bala.

The 36 cards Ahmad has now represent the remaining 3/4 of his original amount.

3/4 of Ahmad's original = 36

1/4 of Ahmad's original = 36 ÷ 3 = 12

4/4 (Ahmad's original total) = 12 × 4 = 48

Final Check

Ahmad starts with 48, Bala starts with 96 (Total: 144).

Ahmad gives 1/4 (12 cards) to Bala → Ahmad: 36, Bala: 108

Bala gives 1/3 (36 cards) to Ahmad → Bala: 72, Ahmad: 72. Correct!

Ahmad had 48 game cards at first.

(a) Complete the square

We rewrite the expression by completing the square:

x² - 6x - 5

Take the coefficient of x, halve it, and square it:

(−6/2)² = 9

Now rewrite:

x² - 6x - 5 = (x−3)² − 9 − 5 = (x−3)² − 14

So the required form is:

(x−3)² − 14

(b) Solve the equation

Using the result from (a):

(x−3)² − 14 = 0

(x−3)² = 14

x − 3 = ±√14

x = 3 ± √14

Final Answers:

(a) (x−3)² − 14

(b) x = 3 ± √14

(a) Completing the Square

To express x² - 6x - 5 in the form (x - a)² - b, we use the method of completing the square.

Identify the coefficient of x: The coefficient is -6.

Divide by 2 and square it: (−6/2)² = (−3)² = 9

Add and subtract this value within the expression:

x² - 6x + 9 - 9 - 5

Simplify into the required form:

The first three terms form a perfect square: (x - 3)².

(x - 3)² - 9 - 5

(x - 3)² - 14

Result: x² - 6x - 5 = (x - 3)² - 14

(b) Solving the Equation

Now, we use the completed square form to solve x² - 6x - 5 = 0:

Set the expression to zero:

(x - 3)² - 14 = 0

Move the constant to the other side:

(x - 3)² = 14

Take the square root of both sides:

x - 3 = ±√14

Isolate x:

x = 3 ± √14

Result: The solutions are 3 ± √14.

a) Definition of electromotive force (e.m.f.)

The electromotive force (e.m.f.) of a battery is the energy supplied by the battery per unit charge as it drives charge around a circuit.

(b) Useful power output of the motor

First find the work done in lifting the block:

Work done = mgh = 2.5 × 9.8 × 4.0 = 98 J

Now calculate power:

Power = Work done / time = 98 / 5.0 = 19.6 W

Final answer:

(a) Energy supplied per unit charge

(b) 19.6 W

a) Electromotive Force (e.m.f.)

The electromotive force (e.m.f.) of a battery is the total work done by the battery in driving a unit charge around a complete circuit. It is measured in volts (V), where 1 volt is equal to 1 joule per coulomb.

(b) Calculating Useful Power Output

To find the useful power output, we first need to determine the work done by the motor to lift the block and then divide that by the time taken.

1. Calculate the Work Done (Gain in Potential Energy)

When the motor lifts the block at a constant speed, the work done is equal to the gain in gravitational potential energy:

Ep = mgh

Where m = 2.5 kg, g ≈ 9.8 m/s² (standard gravity), h = 4.0 m

Ep = 2.5 × 9.8 × 4.0 = 98 J

(Note: If using g = 10 m/s² for simplicity, the energy would be 100 J).

2. Calculate the Power Output

P = Work / time = 98 / 5.0 = 19.6 W

Result: The useful power output of the motor is 19.6 W.

(a) Avogadro's Law

Avogadro's Law states that equal volumes of gases, at the same temperature and pressure, contain equal numbers of molecules.

(So, volume ratios only apply to gases, not solids or solutions.)

(b) Explanation of the error

The student's claim is mathematically incorrect because they are incorrectly applying gas volume relationships to a solution (aqueous HCl).

The 24 dm³ given refers to hydrochloric acid in aqueous form (aq), not a gas.

Avogadro's Law (and simple volume ratios like 2:1 → 24 dm³ : 12 dm³) only applies when all substances are gases under the same conditions.

In this reaction:

HCl is aqueous (dissolved in water)

Mg is a solid

Only H₂ is a gas

So, the volume of acid does not directly represent the number of moles unless its concentration is known.

Correct reasoning:

To find the volume of hydrogen gas produced, you must:

Use the concentration and volume of HCl to find moles of HCl

Use the mole ratio (2:1) to find moles of H₂

Then convert moles of gas to volume (at r.t.p.)

Key point:

The student wrongly assumed that volume ratios apply to aqueous solutions, but they only apply to gases, so the conclusion of 12 dm³ is invalid.

(a) Avogadro's Law

Avogadro's Law states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules (or moles).

(b) Explanation of the Student's Claim

The student's claim is mathematically incorrect because they are applying the molar volume of a gas to a liquid solution.

1. Molar Volume vs. Concentration

The 24 dm³ refers to the volume of aqueous hydrochloric acid (HCl (aq)), not a gas.

In chemistry, the rule that 1 mole = 24 dm³ at r.t.p. applies only to gases.

For an aqueous solution, the number of moles depends on its concentration (moles = concentration × volume), which is not provided here.

2. States of Matter and Molar Ratios

While the stoichiometric ratio in the equation is indeed 2:1 (2 moles of HCl produce 1 mole of H₂), you cannot compare the volume of a liquid/solution directly to the volume of a gas using that ratio.

The 24 dm³ of liquid acid does not contain 1 mole of HCl molecules unless the concentration happens to be exactly 1/24 mol/dm³.

If the acid were a gas (HCl (g)) at r.t.p., the student would be correct. However, because it is (aq) (aqueous), the volume of the solution is mostly water and does not represent the molar quantity of the solute in the same way a gas volume does.

Conclusion: The student is incorrectly treating the volume of a solution as if it were the volume of a gas.