Question

assume that each tablet’s mass was 1,000 mg, and remember that you used 0.200 l of water each time. compute the reaction rate to the nearest whole number using the formula below. reaction rate = (mass of tablet / volume of water) / reaction time 3°c reaction time = 138.5 sec reaction rate = 36 mg/l/sec 24°c reaction time = 34.2 sec reaction rate = 146 mg/l/sec 40°c reaction time = 26.3 sec reaction rate = 190 mg/l/sec 65°c reaction time = 14.2 sec reaction rate = 352 mg/l/sec full tablet reaction time = 34.5 sec reaction rate = □ mg/l/sec eight pieces reaction time = 28.9 sec reaction rate = □ mg/l/sec tiny pieces reaction time = 23.1 sec reaction rate = □ mg/l/sec

Explanation:

Step1: Full tablet reaction rate

Given mass of tablet = 1000 mg, volume of water = 0.200 L, reaction time = 34.5 sec.
Using the formula \( \text{Reaction Rate} = \frac{\text{mass of tablet / volume of water}}{\text{reaction time}} \), first calculate mass/volume: \( \frac{1000}{0.200} = 5000 \) mg/L.
Then divide by reaction time: \( \frac{5000}{34.5} \approx 145 \) (rounded to nearest whole number). Wait, wait, maybe I miscalculated. Wait, formula is (mass/volume)/time = mass/(volume*time). So mass is 1000 mg, volume 0.200 L, time 34.5 sec. So \( \frac{1000}{0.200 \times 34.5} = \frac{1000}{6.9} \approx 145 \)? Wait no, 0.200*34.5 = 6.9? Wait 0.2*34.5 = 6.9? Yes. Then 1000/6.9 ≈ 144.927, so 145? Wait but maybe I misread the formula. Wait the formula is (mass of tablet / volume of water) divided by reaction time. So (1000 / 0.200) is 5000 mg/L, then divided by 34.5 sec: 5000 / 34.5 ≈ 144.927, so 145.

Step2: Eight pieces reaction rate

Mass is still 1000 mg (since it's a tablet broken into eight pieces, total mass same), volume 0.200 L, reaction time 28.9 sec.
So \( \frac{1000}{0.200 \times 28.9} = \frac{1000}{5.78} \approx 173 \) (1000/5.78 ≈ 173.01).

Step3: Tiny pieces reaction rate

Mass 1000 mg, volume 0.200 L, reaction time 23.1 sec.
\( \frac{1000}{0.200 \times 23.1} = \frac{1000}{4.62} \approx 216 \) (1000/4.62 ≈ 216.45).

Wait, maybe I made a mistake in the first step. Let's recalculate full tablet:

Full tablet: mass 1000 mg, volume 0.2 L, time 34.5 s.

Reaction Rate = (1000 / 0.2) / 34.5 = 5000 / 34.5 ≈ 144.927 ≈ 145.

Eight pieces: (1000 / 0.2) / 28.9 = 5000 / 28.9 ≈ 173.01 ≈ 173.

Tiny pieces: (1000 / 0.2) / 23.1 = 5000 / 23.1 ≈ 216.45 ≈ 216.

Wait but maybe the formula is (mass)/(volume * time). So mass is 1000 mg, volume 0.2 L, time in sec. So 1000 / (0.2 * t) = 5000 / t.

So for full tablet, t=34.5: 5000/34.5 ≈ 144.9 ≈ 145.

Eight pieces, t=28.9: 5000/28.9 ≈ 173.0.

Tiny pieces, t=23.1: 5000/23.1 ≈ 216.4 ≈ 216.

Wait but let's check the left side. For 3°C, reaction time 138.5 sec: (1000)/(0.2*138.5) = 1000/27.7 ≈ 36, which matches the given 36. Oh! Wait, I see my mistake. The formula is (mass) / (volume * reaction time). So mass is 1000 mg, volume 0.200 L, so volume*time is 0.200 * t. So for 3°C: 1000 / (0.200 * 138.5) = 1000 / 27.7 ≈ 36, which is correct. So my earlier mistake was in the formula interpretation. So the correct formula is Reaction Rate = mass / (volume * reaction time). So mass is 1000 mg, volume 0.200 L, so 1000 / (0.200 * t) = 5000 / t. Wait no: 1000 divided by (0.2 * t) is (1000 / 0.2) / t = 5000 / t. Yes, that's correct. So for 3°C, t=138.5: 5000 / 138.5 ≈ 36, correct. For 24°C, t=34.2: 5000 / 34.2 ≈ 146, correct. For 40°C, t=26.3: 5000 / 26.3 ≈ 190, correct. For 65°C, t=14.2: 5000 / 14.2 ≈ 352, correct. So the formula is 5000 / t, where t is reaction time in seconds.

So now, for full tablet: t=34.5 sec. So 5000 / 34.5 ≈ 144.927 ≈ 145.

Eight pieces: t=28.9 sec. 5000 / 28.9 ≈ 173.01 ≈ 173.

Tiny pieces: t=23.1 sec. 5000 / 23.1 ≈ 216.45 ≈ 216.

Wait but let's recalculate:

Full tablet: 5000 / 34.5. Let's do 34.5 * 145 = 34.5*140 + 34.5*5 = 4830 + 172.5 = 5002.5, which is very close to 5000. So 145 is correct (since 34.5*144 = 34.5*140 + 34.5*4 = 4830 + 138 = 4968, 5000-4968=32, 32/34.5≈0.927, so 144.927≈145).

Eight pieces: 5000 / 28.9. 28.9*173 = 28.9*(170+3)=28.9*170=4913, 28.9*3=86.7, total 4913+86.7=4999.7, which is almost 5000. So 173.

Tiny pieces: 5000 / 23.1. 23.1*216 = 23.1*(200+16)=4620 + 369.6=4989.6. 5000-4989.6=10.4. 10.4/23.1≈0.45, so 216.45≈216.

So:

Full tablet reaction rate: 145 mg/L/sec (wait, but let's check with calculator: 5000 ÷ 34.5 = 144.92753623188406 ≈ 145.

Eight pieces: 5000 ÷ 28.9 = 173.01038062283737 ≈ 173.

Tiny pieces: 5000 ÷ 23.1 = 216.44991341991343 ≈ 216.

Answer:

Full tablet: 145 mg/L/sec
Eight pieces: 173 mg/L/sec
Tiny pieces: 216 mg/L/sec

(Wait, but maybe the problem expects using the same formula as the left side, where for 3°C, it's 1000/(0.2138.5)=36. So for full tablet: 1000/(0.234.5)=1000/6.9≈144.927≈145. Yes, that's the same as 5000/34.5. So correct.)