Would you please tell me if these are right?
A sample of helium has a volume of 325 ml and a pressure of 655 mm hg. What will be the pressure if the helium is compressed to 125 ml (t and n are constant)
I got 1703 mm of Hg
A 75.0 ml sample of oxygen has a pressure of 1.50 atm. what will be the new volume if the pressure becomes 4.50 atm? (t and n constant)
I got 25 mL.
In a weather report, the atmospheric pressure is given as 29.4 inches of Hg. what is the corresponding pressure in mm Hg?
I got 735 mm
Both are correct.
To calculate the new pressure when helium is compressed, you can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature and moles are held constant. The formula for Boyle's Law is as follows:
P1 * V1 = P2 * V2
Where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.
Given:
Initial volume (V1) = 325 ml
Initial pressure (P1) = 655 mmHg
Final volume (V2) = 125 ml
Final pressure (P2) = ?
Using the formula, we can rearrange it to solve for P2:
P2 = (P1 * V1) / V2
Substituting the values:
P2 = (655 mmHg * 325 ml) / 125 ml
P2 = 1697 mmHg (rounded to the nearest whole number)
So the correct answer would be 1697 mmHg, not 1703 mmHg.
For the second question, to find the new volume, you can again use Boyle's Law, rearranging the formula as follows:
P1 * V1 = P2 * V2
Given:
Initial volume (V1) = 75.0 ml
Initial pressure (P1) = 1.50 atm
Final pressure (P2) = 4.50 atm
Final volume (V2) = ?
Using the formula:
V2 = (P1 * V1) / P2
Substituting the values:
V2 = (1.50 atm * 75.0 ml) / 4.50 atm
V2 = 25.0 ml
So the correct answer is indeed 25 mL.
Regarding the conversion from inches of Hg to mm Hg, 1 inch of Hg is equivalent to 25.4 mm Hg. Therefore, to convert 29.4 inches of Hg to mm Hg, we can multiply it by 25.4:
29.4 inches of Hg * 25.4 mm Hg/inch = 744.76 mm Hg
Rounded to the nearest whole number, we get 745 mmHg, not 735 mmHg.
So in summary, the corrected answers would be:
1. The pressure will be 1697 mmHg.
2. The new volume will be 25 mL.
3. The corresponding pressure in mm Hg would be 745 mmHg.
To solve the first problem, where a sample of helium is compressed from a volume of 325 ml to 125 ml while keeping temperature and amount of gas constant, you can use Boyle's Law. Boyle's Law states that the product of pressure and volume is constant for a given amount of gas at a constant temperature.
Using Boyle's Law equation, we have P1 x V1 = P2 x V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Plugging in the given values:
P1 = 655 mm Hg
V1 = 325 ml
V2 = 125 ml
Let's solve for P2:
P2 = (P1 x V1) / V2
P2 = (655 mm Hg x 325 ml) / 125 ml
P2 = 1697 mm Hg
So, the pressure of the helium after compression is approximately 1697 mm Hg, not 1703 mm Hg as you obtained. This may be a minor rounding difference.
For the second problem with the oxygen sample, to find the new volume when the pressure changes from 1.50 atm to 4.50 atm while keeping temperature and amount of gas constant, you can use the combined gas law or the ideal gas law.
The combined gas law states that P1 x V1 / T1 = P2 x V2 / T2, where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2, V2, and T2 are the final pressure, volume, and temperature.
Since the question specifies that the temperature is constant (t constant), we can simplify the equation to P1 x V1 = P2 x V2.
Plugging in the given values:
P1 = 1.50 atm
V1 = 75.0 ml
P2 = 4.50 atm
Let's solve for V2:
V2 = (P1 x V1) / P2
V2 = (1.50 atm x 75.0 ml) / 4.50 atm
V2 = 25.0 ml
So, the new volume of the oxygen sample, when the pressure becomes 4.50 atm, is indeed 25.0 mL, as you correctly obtained.
For the third problem, converting atmospheric pressure in inches of Hg to mm of Hg, you can use the conversion factor that 1 inch of Hg is approximately equal to 25.4 mm of Hg.
Given that the atmospheric pressure is 29.4 inches of Hg, we can multiply this by the conversion factor to get the corresponding pressure in mm of Hg:
29.4 inches of Hg x 25.4 mm of Hg / 1 inch of Hg = 745.2 mm of Hg
So, the corresponding pressure in mm of Hg is approximately 745.2 mm, not exactly 735 mm as you obtained. Again, this may be a minor rounding difference.