using the gas laws, What is V in the table below?
initial: 1420 torr 75 mL 200 K
Final: 760 torr V 360 K
What is T using the gas laws?
Initial: 91.8 mL 365 K
Final: 45.8 mL T
For the first one,
(P1V1/T1) = (P2V2/T2)
For #2, (V1/T1) = (V2/T2)
Don't forget, in both, T is in Kelvin.
To determine the missing variable in the gas laws, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Let's use this equation to solve for the missing variable.
1. Identify the given values:
Initial:
P1 = 1420 torr
V1 = 75 mL
T1 = 200 K
Final:
P2 = 760 torr
V2 = unknown (V)
T2 = 360 K
2. Substitute the known values into the equation:
(1420 torr * 75 mL) / 200 K = (760 torr * V) / 360 K
3. Simplify the equation:
75 * 1420 / 200 = 760 * V / 360
4. Solve for V:
(75 * 1420 * 360) / (200 * 760) = V
V ≈ 56 mL
Therefore, the value of V is approximately 56 mL.
Now, let's proceed to solve for the missing variable T using the same steps.
1. Identify the given values:
Initial:
V1 = 91.8 mL
T1 = 365 K
Final:
V2 = 45.8 mL
T2 = unknown (T)
2. Substitute the known values into the equation:
(91.8 mL * 365 K) / (T1) = (45.8 mL * T) / (T2)
3. Simplify the equation:
91.8 * 365 / 365 = 45.8 * T / T2
4. Solve for T:
(91.8 * 365 * T2) / (365 * 45.8) = T
T ≈ 45.8 K
Therefore, the value of T is approximately 45.8 K.
To determine the value of V in the given table using the gas laws, we can use the combined gas law, which states:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
We are given the following values:
Initial:
P1 = 1420 torr
V1 = 75 mL
T1 = 200 K
Final:
P2 = 760 torr
V2 = ?
T2 = 360 K
Using the combined gas law, we can rearrange the formula to solve for V2:
V2 = (P1 * V1 * T2) / (P2 * T1)
Plugging in the given values:
V2 = (1420 torr * 75 mL * 360 K) / (760 torr * 200 K)
Now, we can calculate the value of V2:
V2 = 2.83 mL
Therefore, V is approximately 2.83 mL in the given table.
Now, let's move on to determining the value of T in the second table using the gas laws. We can use the same combined gas law formula:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
We are given the following values:
Initial:
P1 = 91.8 mL
V1 = 365 K
Final:
P2 = 45.8 mL
V2 = ?
T2 = T (unknown)
Rearranging the formula to solve for T2:
T2 = (P2 * V2 * T1) / (P1 * V1)
Plugging in the given values:
T2 = (45.8 mL * 365 K) / (91.8 mL)
Now, we can calculate the value of T2:
T2 = 182.9 K
Therefore, T is approximately 182.9 K in the given table.