Question

A sample of ammonia occupies 0.250 L under laboratory conditions of 27°C and 0.850 atm. Find the volume of this sample at 0°C and 1.00 atm. Give your answer to 3 significant figures

Answer 1

The final volume of the ammonia sample is 0.193 L (3 s.f.).

Step-by-step explanation:

To find the final volume of the sample of ammonia, we can use the combined gas law.

Combined Gas Law

`\boxed{\sf (P_1V_1)/(T_1)=(P_2V_2)/(T_2)}`

where:

• P₁ is the initial pressure.
• V₁ is the initial volume.
• T₁ is the initial temperature (in kelvin).
• P₂ is the final pressure.
• V₂ is the final volume.
• T₂ is the final temperature (in kelvin).

First, convert the temperatures from Celsius to kelvin by adding 273.15:

`\implies \sf T_1 = 27^(\circ)C + 273.15 = 300.15\;K`

`\implies \sf T_2 = 0^(\circ)C + 273.15 = 273.15\;K`

Therefore, the values are:

• P₁ = 0.850 atm
• V₁ = 0.250 L
• T₁ = 300.15 K
• P₂ = 1.00 atm
• T₂ = 273.15 K

Substitute the values into the formula and solve for V₂:

`\implies \sf (0.850 \cdot 0.250)/(300.15)=(1.00 \cdot V_2)/(273.15)`

`\implies \sf V_2=(0.850 \cdot 0.250 \cdot 273.15)/(300.15 \cdot 1.00)`

`\implies \sf V_2=0.1933845...`

`\implies \sf V_2=0.193\;L\;(3\;s.f.)`

Therefore, the final volume of the ammonia sample at 0°C and 1.00 atm is approximately 0.193 L (3 s.f.).