Question

В сосуд с водой со скоростью 10 мл/мин начинают добавлять приготовленный раствор, содержащий 3% соли, и через 1 мин. получают новый раствор содержащий 0,3% соли. Найти каким будет процентное содержание соли в новом растворе через 6 мин. после начала добавления приготовленного раствора.

Answer 1

Узнаем  изначальную массу воды в сосуде
(10*0.03)/(x+10)=0.003
0,3/(х+10)=0,003
х+10=0,3/0,003
х+10=100
х=100-10
х=90 мл
а теперь всё просто
(6*10*0,03)/(6*10+90)*100=1,2%

Answer 2

Problem Analysis

We are given a vessel containing water, and we are adding a prepared solution containing 3% salt to the vessel at a rate of 10 ml/min. After 1 minute, we obtain a new solution containing 0.3% salt. We need to find the percentage of salt in the new solution after 6 minutes of adding the prepared solution.

Solution

To solve this problem, we can use the concept of the method of mixtures. The amount of salt in the vessel at any given time can be calculated by considering the rate of addition of the prepared solution and the rate of dilution due to the addition of water.

Let's assume that after 1 minute, the volume of the new solution in the vessel is V1 ml and the percentage of salt in the new solution is P1%. We are given that V1 = 10 ml and P1 = 0.3%.

After 6 minutes, the volume of the new solution in the vessel will be V2 ml, and we need to find the percentage of salt in the new solution, P2%.

To find P2%, we can use the following equation:

P1 * V1 = P2 * V2

Substituting the given values:

0.3% * 10 ml = P2% * V2

Simplifying the equation:

0.003 * 10 = P2% * V2

0.03 = P2% * V2

Now, we need to find the value of V2. Since the prepared solution is being added at a rate of 10 ml/min, after 6 minutes, the total volume of the new solution in the vessel will be:

V2 = V1 + (rate of addition * time)

Substituting the given values:

V2 = 10 ml + (10 ml/min * 6 min)

V2 = 10 ml + 60 ml

V2 = 70 ml

Now, we can substitute the value of V2 into the equation to find P2:

0.03 = P2% * 70 ml

Simplifying the equation:

P2% = 0.03 / 70 ml

P2% ≈ 0.0004286 ≈ 0.043%

Therefore, the percentage of salt in the new solution after 6 minutes of adding the prepared solution is approximately 0.043%.

Conclusion

The percentage of salt in the new solution after 6 minutes of adding the prepared solution is approximately 0.043%.