the volume of a sample of helium is 4.5ml at 20.0c and 203.0kpa. what will its volume be in the figure?
4.34ml
To find the volume of the sample of helium in the given figure, we need to use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in kPa)
V = Volume (in mL)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K for easier unit conversion)
T = Temperature (in Kelvin)
First, we need to convert the given volume from mL to L:
4.5 mL = 4.5/1000 L = 0.0045 L
Now, we can rearrange the ideal gas law equation to solve for the new volume (V2) at a different temperature and pressure:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Let's assign the given values to the variables:
P1 = 203.0 kPa
V1 = 0.0045 L
T1 = 20.0 °C = 20.0 + 273.15 = 293.15 K
P2 = pressure in the given figure
T2 = temperature in the given figure (in Kelvin)
Now we can solve for V2:
(203.0 * 0.0045) / (293.15) = (P2 * V2) / (T2)
Let's say the pressure in the given figure is P2 = 150.0 kPa. Plugging in the values:
(203.0 * 0.0045) / (293.15) = (150.0 * V2) / (T2)
Now, you can rearrange the equation to solve for V2:
V2 = [(203.0 * 0.0045) / (293.15)] * (T2 / 150.0)
Remember to convert the temperature in the given figure (if it's given in Celsius) to Kelvin before plugging it into the equation.
To determine the volume of the sample of helium in the given conditions, we need to use the ideal gas law. The ideal gas law equation is:
PV = nRT
where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
First, we need to convert the temperature from Celsius to Kelvin. The relationship between Celsius and Kelvin is given by:
T(K) = T(C) + 273.15
Given that the temperature is 20.0°C, we can convert it to Kelvin:
T(K) = 20.0 + 273.15 = 293.15 K
Next, we have the following information:
Initial volume: V1 = 4.5 mL
Initial temperature: T1 = 293.15 K
Initial pressure: P1 = 203.0 kPa
Final volume: V2 = ?
Now, we need to rearrange the ideal gas law equation to solve for V2:
V2 = (P1 * V1 * T2) / (P2 * T1)
To find P2, which is the final pressure, we need to make an assumption that the amount of gas (number of moles) and temperature remain constant. Therefore, P2 is directly proportional to V2:
P2 = (V2 * P1) / V1
Substituting this value of P2 back into the rearranged equation, we get:
V2 = (P1 * V1 * T2) / (V1 * T1)
Canceling out the V1 terms, we get:
V2 = (P1 * T2) / T1
Now we can substitute the given values into the equation to find V2:
V2 = (203.0 kPa * 293.15 K) / 293.15 K
V2 = 203.0 kPa
Therefore, the volume of the sample of helium will be 203.0 mL.