You will use the formula pV = kBNT to find the depth of the box (front to back measurement). The volume of the box is given by the formula V = W H * D. (You will need to convert the pressure from atm to Pa, or pascals, by multiplying atms by 1 * 105.)

Question

You will use the formula pV = kBNT to find the depth of the box (front to back measurement). The volume of the box is given by the formula V = W H * D. (You will need to convert the pressure from atm to Pa, or pascals, by multiplying atms by 1 * 105.)

The height of the chamber is 5.30nm
the width is 6.5nm

Please help!

Answer 1

To find the depth of the box (front to back measurement) using the given information, we can use the ideal gas law:

p * V = n * R * T

Where:
p = pressure in pascals (Pa)
V = volume in cubic meters (m^3)
n = number of moles (mol)
R = gas constant (8.314 J/(mol*K))
T = temperature in kelvin (K)

However, we need to convert the pressure from atm to pascals before using the formula. 1 atm is equal to 1 * 10^5 pascals, so we multiply the given pressure by 1 * 10^5 to convert it to pascals.

Given information:
Height (H) = 5.30 nm
Width (W) = 6.5 nm

The volume of the box (V) is given by the formula V = W * H * D, where D is the depth we are trying to find.

To find D, we can rearrange the volume formula as follows:
D = V / (W * H)

Now, we need to find the volume (V) using the ideal gas law. Since we are only interested in the depth (D) and not the actual number of moles, we can set n = 1 (assume 1 mole of gas).

Substituting the given values into the ideal gas law:

P * V = n * R * T

P (pressure in pascals) = given pressure in atm * 1 * 10^5 pascals
V (volume in m^3) = W (width in meters) * H (height in meters) * D (depth in meters)
n = 1 (since we assume 1 mole of gas)
R (gas constant) = 8.314 J/(mol*K)
T (temperature in kelvin) = given temperature

Rearranging the equation for V:

V = (P / (n * R * T)) * (W * H * D)

Substituting the values and the given information into the equation:

(P * V) = (1 * 10^5 * W * H * D) = (1 * 8.314 * T)
1 * 10^5 * 6.5 * 5.30 * D = 8.314 * T

Simplifying the equation:

D = (8.314 * T) / (1 * 10^5 * 6.5 * 5.30)

D = (0.008314 * T) / (3.0685)

Therefore, the depth of the box (front to back measurement) can be found by dividing 0.008314 multiplied by the given temperature (T in Kelvin) by 3.0685.

You will use the formula p*V = kB*N*T to find the depth of the box (front to back measurement). The volume of the box is given by the formula V = W * H * D. (You will need to convert the pressure from atm to Pa, or pascals, by multiplying atms by 1 * 105.)

To find the depth of the box (front to back measurement) using the given information, we can use the ideal gas law:

You will use the formula pV = kBNT to find the depth of the box (front to back measurement). The volume of the box is given by the formula V = W H * D. (You will need to convert the pressure from atm to Pa, or pascals, by multiplying atms by 1 * 105.)