The volume of a gas is 17.5 mL at 29◦C and

0.863 atm. What will the volume be at 13◦C

and 0.994 atm?

Answer: V = 14.4 mL

Explanation:

In this case, we'll use the ideal gas formula:

PV = nRT

Where:

P: pressure in atm

V: volume in liter

n: moles

R: gas constant (In this case 0.082 L atm/mol K)

T: temperature in K

We have data for the gas at first, so we can actually calculate the moles used, which will be constant even at different temperature and pressure. Let's calculate the moles:

n = PV/RT

Before we do this, let's convert the volume and temperature:

T = 29 + 273 = 302 K

V = 17.5 / 1000 = 0.0175 L

Now the moles:

n = 0.863 * 0.0175 / 0.082 * 302 = 0.00061 moles

with these moles, let's convert the temperature to K:

T2 = 13 + 273 = 286 K

and to calculate the volume:

V = nRT/P

so:

V = 0.00061 * 0.082 * 286 / 0.994

V = 0.0144 L or simply 14.4 mL