According to the given information, substance B (B_t) is related to substance A (A_t) as follows: B_t = A_t^2.
We also know that after 60 minutes, the amount of substance A has decreased from 48 grams to 15 grams. So, at t = 60 minutes, A_t = 15 grams.
Now, let's calculate the initial amount of substance A (A_0) in grams:
A_0 = B_0^(1/2) [Since B_0 = A_0^2]
48 = A_0^2
A_0 = √48
A_0 ≈ 6.93 grams (rounded to two decimal places)
Now, we can draw the graph of the remaining amount of substance A (A_t) versus time (t) for t = 150, 160, 170, and 180 minutes.
Time (t) | Amount of A remaining (A_t)
60 mins | 15 grams
150 mins | ?
160 mins | ?
170 mins | ?
180 mins | ?
To find A_t at 150, 160, 170, and 180 minutes, we use the relation between A_t and B_t:
B_t = A_t^2
We also know that the initial amount of substance A (A_0) is approximately 6.93 grams.
Let's calculate A_t at different time intervals:
At t = 150 minutes:
B_150 = 15 grams (from t = 60 mins)
A_150 = √B_150 ≈ √15 ≈ 3.87 grams
At t = 160 minutes:
B_160 = A_160^2
B_160 = B_150 - (rate constant * B_150 * 10 mins) [Since 160 mins - 150 mins = 10 mins]
B_160 = 15 - (rate constant * 15 * 10)
B_160 = 15 - (rate constant * 150)
A_160 = √B_160
Similarly, at t = 170 and 180 minutes, we can find A_t using the same method.
Once you have the values of A_t at different time intervals, you can plot them on a graph with time on the x-axis and the amount of substance A remaining on the y-axis. Connect the points to get a smooth curve.
Step-by-step explanation:
Graph of A Remaining.
User
a certain chemical reaction, a substance (A) is converted into another substance (B) according to the following rate proportional: B = A^2 After 60 minutes, the amounts of substance has decreased from 48 grams to 15 grams. Draw a graph between the amount of the first substance remaining and time (after 150, 160, 170, 180 minutes).
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To draw the graph between the amount of substance A remaining and time, we need to first find the relationship between the amount of substance A (A_t) at time t and the initial amount of substance A (A_0).
According to the given information, substance B (B_t) is related to substance A (A_t) as follows: B_t = A_t^2.
We also know that after 60 minutes, the amount of substance A has decreased from 48 grams to 15 grams. So, at t = 60 minutes, A_t = 15 grams.
Now, let's calculate the initial amount of substance A (A_0) in grams:
A_0 = B_0^(1/2) [Since B_0 = A_0^2]
48 = A_0^2
A_0 = √48
A_0 ≈ 6.93 grams (rounded to two decimal places)
Now, we can draw the graph of the remaining amount of substance A (A_t) versus time (t) for t = 150, 160, 170, and 180 minutes.
Time (t) | Amount of A remaining (A_t)
60 mins | 15 grams
150 mins | ?
160 mins | ?
170 mins | ?
180 mins | ?
To find A_t at 150, 160, 170, and 180 minutes, we use the relation between A_t and B_t:
B_t = A_t^2
We also know that the initial amount of substance A (A_0) is approximately 6.93 grams.
Let's calculate A_t at different time intervals:
At t = 150 minutes:
B_150 = 15 grams (from t = 60 mins)
A_150 = √B_150 ≈ √15 ≈ 3.87 grams
At t = 160 minutes:
B_160 = A_160^2
B_160 = B_150 - (rate constant * B_150 * 10 mins) [Since 160 mins - 150 mins = 10 mins]
B_160 = 15 - (rate constant * 15 * 10)
B_160 = 15 - (rate constant * 150)
A_160 = √B_160
Similarly, at t = 170 and 180 minutes, we can find A_t using the same method.
Once you have the values of A_t at different time intervals, you can plot them on a graph with time on the x-axis and the amount of substance A remaining on the y-axis. Connect the points to get a smooth curve.