The method: keep the two gas states together
The combined gas law compares a fixed amount of gas before and after a change. Use it here to model the gas in the balloon up to the moment it bursts, before gas escapes.
P₁V₁ / T₁ = P₂V₂ / T₂
The subscript 1 means the initial state; 2 means the final state. P is pressure, V is volume, and T must be absolute temperature in Kelvin. Page 4 of the 2025 tables supplies both this relationship and the conversion K = °C + 273.15.
Use the same pressure unit on both sides and the same volume unit on both sides. When they already match, you can keep them. If pressure is constant, the pressure terms cancel and the relationship becomes V₁/T₁ = V₂/T₂. Here, pressure changes, so keep both pressure values.
Find the formula in our 2025 Reference Tables guide · Open the official tables, page 4
Try the official question
Official NYSED excerpt · August 2026 · Question 42
Selected stimulus needed for this question, from Parade of Balloons. The complete cluster is linked below.
A weather balloon rises through the atmosphere and collects data until it bursts and falls to Earth. A weather balloon containing 155 L of gas is released into the atmosphere from sea level at a standard pressure of 101.3 kPa where the temperature is 25°C. The balloon climbs to an altitude where the atmospheric pressure is 11.6 kPa, and reaches a maximum volume of 1172 L before bursting.
42. Construct a mathematical representation, using appropriate calculations, that could be used to determine the temperature at the point where the weather balloon bursts. Show all work. [1]
Mathematical Representation: Write your setup on paper before reading on.
NYSED exam booklet, page 32 · See the full cluster and question breakdown
Worked reasoning · New Regents explanation
1. Sort the measurements into initial and final states
“Released” gives state 1. The conditions just before bursting give state 2. The unknown is the final temperature, T₂.
| Quantity | Initial (1) | Final (2) |
|---|---|---|
| Pressure | 101.3 kPa | 11.6 kPa |
| Volume | 155 L | 1172 L |
| Temperature | 25°C | T₂ (unknown) |
Both pressures are in kPa and both volumes are in L. No pressure or volume conversion is needed. The word “standard” describes the initial pressure; use the stated initial temperature rather than assuming the balloon starts at STP.
2. Convert the initial temperature to Kelvin
T₁ = 25 + 273.15 = 298.15 K
A Celsius value cannot be used in a gas-law ratio. Kelvin measures temperature from absolute zero, so the ratios describe the gas correctly.
3. Substitute into the combined gas law
This setup keeps each pressure paired with its volume. It shows the relationship and substitution that the question requests.
4. Isolate the unknown, then calculate
T₂ = (P₂V₂T₁) / (P₁V₁)
T₂ ≈ 258.15 K
The kPa and L units cancel between numerator and denominator, leaving K. To express the result in Celsius, subtract 273.15: approximately -15°C. That conversion is extra interpretation; a correctly substituted mathematical representation is the requested work.
5. Check what the result means
The balloon’s volume grows as it rises, but the outside pressure drops sharply. A larger volume alone does not prove a higher temperature. Compare the two P × V products: the final product is smaller, so the final Kelvin temperature should be lower. The calculated result follows that pattern.
What the official scoring guide accepts
The official question is worth one credit and asks for a mathematical representation with work shown. The guide accepts several equivalent setups; it does not require one specific algebraic arrangement.
Official NYSED scoring guidance · Question 42
New Regents interpretation: Show the gas-law relationship with the measurements in the correct places and Kelvin temperature. The official examples show both a precise and a rounded Kelvin conversion. Our numerical evaluation above helps you interpret the setup; it is not an additional scoring requirement.
Common mistakes to catch
- Using Celsius in the ratio. Convert to Kelvin before substituting. Subtract 273.15 only if you want a Celsius interpretation at the end.
- Canceling pressure when it changes. This balloon starts at 101.3 kPa and reaches 11.6 kPa. Keep both values in the combined gas law.
- Mixing the two states. P₁ belongs with V₁ and T₁; P₂ belongs with V₂ and T₂. A before/after table prevents cross-pairing.
- Writing only a final temperature. This prompt requests a mathematical representation and all work. Show the substituted relationship.
Practice the same skill in a full cluster
Return to Parade of Balloons to work the surrounding questions on gas properties and the balloon context. For another gas-law setup, open Balloon Arches and look for the mathematical-representation question.
Full exam clusters in the workspace require New Regents membership. This lesson, its question, and the linked NYSED PDFs are public. Try free official sample practice. You have seen this question’s solution; use the different cluster for a fresh attempt.
August 2026 Chemistry exam, key, and score guide · June 2026 exam guide · Review another Chemistry topic