A 500. mL sample of a gas is collected in a laboratory at a temperature of 293K and a pressure of 720 mmHg. What is the new volume of the gas at STP? Show all work for full credit including units and sig figs.

Question

A 500. mL sample of a gas is collected in a laboratory at a temperature of 293K and a pressure of 720 mmHg. What is the new volume of the gas at STP? Show all work for full credit including units and sig figs.

Answer 1

since PV/T is constant, you want V such that

760V/273 = 720*500/293

Answer 2

To find the new volume of the gas at STP (Standard Temperature and Pressure), we need to use the combined gas law equation:

(P1 × V1) / (T1) = (P2 × V2) / (T2),

where P1 and T1 are the initial pressure and temperature, V1 is the initial volume, P2 and T2 are the final pressure and temperature, and V2 is the final volume.

Given:
P1 = 720 mmHg
V1 = 500 mL
T1 = 293K (Kelvin)

We need to find V2.

Now let's convert the initial volume from milliliters to liters:

V1 = 500 mL = 500/1000 = 0.5 L (rounded to one decimal place)

Next, we need to convert the initial pressure from millimeters of mercury (mmHg) to atmospheres (atm):

P1 = 720 mmHg × (1 atm / 760 mmHg) = 0.9473684211 atm (rounded to 1 decimal place)

Now we can substitute the known values into the combined gas law equation:

(0.9473684211 atm × 0.5 L) / 293K = (1 atm × V2) / 273K

Simplifying the equation:

0.4736842105 atm·L / K = (1 atm × V2) / 273K

Now, let's solve for V2:

V2 = (0.4736842105 atm·L / K × 273K) / 1 atm

V2 = 0.4736842105 L

Therefore, the new volume of the gas at STP is approximately 0.5 L (rounded to one decimal place).

Answer 3

To determine the new volume of the gas at STP (Standard Temperature and Pressure), which is defined as 0°C (273K) and 1 atmosphere (760 mmHg), we can use the combined gas law equation:

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

Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (STP = 1 atm)
V2 = final volume (unknown)
T2 = final temperature (STP = 0°C = 273K)

Let's plug in the given values:
P1 = 720 mmHg
V1 = 500 mL
T1 = 293K

P2 = 1 atm
T2 = 273K

Now, we can solve for V2 by rearranging the equation:

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

Substituting the values:
V2 = [(720 mmHg * 500 mL * 273K) / (1 atm * 293K)]

To make sure we have the correct answer, we need to do unit conversions:

1 atm = 760 mmHg
1 mL = 0.001 L

V2 = [(720 mmHg * 500 mL * 273K) / (760 mmHg * 293K)]
V2 = [(720 * 500 * 273) / (760 * 293)] L

Now, calculate the value:

V2 ≈ 0.830 L

Therefore, the new volume of the gas at STP is approximately 0.830 liters.