A sample of CO2 gas in a syringe has a volume of 25.0 mL at 20.0 ºC. If you warm the gas in your hand to

37 ºC, what will be the final volume?

(V1/T1) = (V2/T2)

Remember T must be in kelvin.

To find the final volume of the CO2 gas, we can use the combined gas law equation:

(P₁V₁) / (T₁) = (P₂V₂) / (T₂)

Where:
P₁ and P₂ are the initial and final pressures (which we assume remain constant)
V₁ is the initial volume (25.0 mL)
T₁ is the initial temperature (20.0 ºC + 273.15 = 293.15 K)
T₂ is the final temperature (37 ºC + 273.15 = 310.15 K)
V₂ is the final volume (which we need to find)

Since the pressure is constant and cancels out on both sides of the equation, we can simplify the formula to:

(V₁) / (T₁) = (V₂) / (T₂)

Now we can rearrange the formula to solve for V₂:

V₂ = (V₁ * T₂) / (T₁)

Substituting the given values into the equation:

V₂ = (25.0 mL * 310.15 K) / (293.15 K)

Calculating the value:

V₂ ≈ 26.45 mL

Therefore, the final volume of the CO2 gas when warmed to 37 ºC will be approximately 26.45 mL.

To calculate the final volume of the CO2 gas when warmed to 37 ºC from 20 ºC, we can use the combined gas law equation:

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

Where:
P1 and P2 are the initial and final pressures of the gas (which remains constant)
V1 is the initial volume of the gas
V2 is the final volume of the gas that we want to find
T1 is the initial temperature of the gas
T2 is the final temperature of the gas

In this case, we know the initial volume (V1) is 25.0 mL, the initial temperature (T1) is 20.0 ºC, and the final temperature (T2) is 37 ºC. Since the pressure remains constant, we can simplify the equation as:

V1 / T1 = V2 / T2

Now, let's plug in the given values:

25.0 mL / 20.0 ºC = V2 / 37 ºC

To find V2, we can cross-multiply and solve for V2:

V2 = (25.0 mL * 37 ºC) / 20.0 ºC
V2 = 46.25 mL

Therefore, the final volume of the CO2 gas when warmed to 37 ºC from 20 ºC will be 46.25 mL.