Solve for the new pressure in each of the following with N and V constant

A sample of Na with a pressure of 770 mmHG at -60C is heated to 23C

24

To solve for the new pressure of a sample of Na when the temperature increases from -60°C to 23°C, we can use the combined gas law equation:

P1 * V1 / T1 = P2 * V2 / T2

where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes (which are given as constant), T1 and T2 are the initial and final temperatures.

Given:
P1 = 770 mmHg
T1 = -60°C
T2 = 23°C

Step 1: Convert temperature from Celsius to Kelvin
To use the equation, we need to convert the temperatures from Celsius to Kelvin. The conversion formula is:
Kelvin = Celsius + 273.15

T1 = -60°C + 273.15 = 213.15 K
T2 = 23°C + 273.15 = 296.15 K

Step 2: Substitute the values into the combined gas law equation
P1 * V1 / T1 = P2 * V2 / T2

P2 = (P1 * V1 * T2) / (V2 * T1)

Since V1 = V2 and N is constant, we can ignore the volume and rewrite the equation as:

P2 = (P1 * T2) / T1

Now, substitute the values:

P2 = (770 mmHg * 296.15 K) / 213.15 K

Step 3: Calculate the new pressure
P2 = (228403 mmHg * K) / K
P2 = 228403 mmHg

Therefore, the new pressure of the sample of Na when it is heated from -60°C to 23°C is approximately 228403 mmHg.